The sticky point might be your wife's substitute teaching. In some schools, I'm not prepared to guess what portion, substitute teaching is not considered anywhere near as valuable as having a class of your own. In my own school, it is not considered teaching experience - we require at least three years full time in your own classroom, and any sub work will not count towards that minimum nor towards placement on the pay scale. So if subbing is the sum total of your wife's experience, we would not be able to hire her. This may hold true for other schools.
How to work around it? Put yourself up as the recruiting teacher, and offer for your wife to come without a contract, with the expectation that she would work as a substitute. If all went well, the school might consider taking her on later as a full-time teacher. In fact, she'd be well placed for an emergency position when someone resigns or gets ill or whatever mid-year.
Or focus on schools that are a bit lower quality. Their hiring rules might be more relaxed.
Good luck.

One can never really understand what it's like to live in another's perspective, but I'm really glad I don't believe that everyone out there is selfish, scheming, mean and immoral. It seems to me like it would be painful and depressing. And how much energy it must take up...

If you know Boston, that's a completely different kettle of fish. Good luck.

Dress professionally and fairly formally throughout. As said before, you are 'on' the whole time you're there, and you don't want to be caught out when you have a chance meeting with the recruiter from your dream school. So, unless you're actively checking in/out, with a suitcase in hand, dress the part.

Print your CVs etc before you come. Boston is a big city, and the hotel isn't exactly in the heart of a walking business district, certainly not in Feb. You're leaving yourself open for a very stressful, expensive and potentially unsuccessful day if you set out in search of a Kinko's. What if there's an issue and you have to change layout, etc? Nope, too risky for me. I'd be a bundle of nerves.

It never hurts to try and you wouldn't be the first person to succeed.
However, schools will tend to prefer math teachers who can teach the full gamut, or most of it, and by 'can' I mean have demonstrated that they can in one way or another. In the short term, if a school is pinched and needs to hire someone, they may hire someone who can only teach through middle school, but year after year that hiring choice will drive scheduling decisions and hiring needs, and the recruiter knows that, so he will avoid it if he can.
Smaller schools, with only 1 math teacher for all middle and high grades, obviously can't make such a choice at all. Even in a bigger school with 6 or 12 math teachers, the knock-on effects of such a choice can be far-reaching, and it's a drain on morale and resources when 'we'd like to have you teach x course, but we can't because Mr Middle School can't be moved'.

So what am I saying? Give it a go, it can't hurt, but be understanding when schools are not fully enthusiastic. And maybe have some solutions in mind to ease their worries, like a plan for how you will take some graduate courses to prepare you for higher math courses in the coming years.

I'd skip hotmail or yahoo and go for gmail. The first two sometimes have issues in different countries and can be shunted to junk mail or not delivered.

As a recruiter, I don't really have a priority list of what's most important. I'm looking at the whole package. What can you teach, what's your experience, what's your credentials, what do your referees say (both in letters and when I call them), what schools have you been in, how long did you stay, what's your family situation, how reflective are you about your practice and what does your reflection tell me about your suitability for our school, etc, etc. Any piece of that can be a bonus or a hindrance.

I'd base my decision on somewhat different factors.
First, which school was it, and what is their general reputation? Not what do you think of them, which is obviously not much, but what do most people think of them? If they're known as a bad school, they can't do too much damage to you. People will understand, mostly, even though runners are not popular. Don't expect a tier one school to hire you in these conditions, unless you really stand out as an excellent candidate otherwise. And if they're known as a good school, you've got real problems.

Second, who will be at the fair as the school's representative? Was it the guy who was in charge when you left? Or has leadership changed? What does the actual current recruiter know about you, if anything? Maybe he wasn't even there, in which case he probably won't recognize your name, and you have nothing to fear from him.

Third, where is the guy or guys who were in charge when you left? If they've moved on to other schools, they can still do you damage, particularly if they are now at schools with better reputations.

Fourth, what is the nature of the guy or guys who were in charge? Are they likely to be vindictive? How badly did you upset them?

It's hard to tell from the outside exactly what the damage could be, since we don't know exactly what happened. There are runners and then there are runners, and I've seen those that were justified and those that were not, mostly those that were not. I'm not judging yours since I don't know the details, but those details will make a huge difference in what could happen at a fair. Personally, I know some people who ran from schools I was at, that if they turned up at a fair, I'd leave them to the job as much as possible and if asked, would give a reasonable review of the situation - in short, I'd actively try not to scupper their chances. But I know some others that if they turned up, I'd be less supportive. It all depends on exactly what happened.

She needs to attend if she's looking for a job. Yes, she's an easier fit, but schools take every position seriously. They will want to see that she's the right candidate for the job.

As a recruiter, I prefer to meet trailing spouses. It's not always possible, sometimes they're home holding down the fort during the fair, but if they're anywhere nearby, make their presence known. Ask the recruiter if they would like your husband to attend the interview, instead of waiting to be asked. They can easily say no, but at least they'll know you're open to it. Make sure your husband attends the social with you, and preferably interview sign-up. Even seeing him for those 3 minutes can help assure the recruiter that all is well.
It's important to give the impression that your husband supports you and your move overseas. That's his main role if he's to be at home, and his starting point if he'll be transitioning into some kind of teaching, so he might as well start right away.

Truth. Some schools have resignation dates as late as June. It's a nightmare for recruiting, but tends to be an offshoot of national law, so nothing a school can do, unless they can afford bonuses for early notifiers, which encourages decisions but doesn't force them.
Other schools have Jan 31 dates, or mid Feb.
And some recruiters will let their teachers delay a decision if its someone they really want to keep. Which would make the incumbent first choice, and you second, but it's not really apples and apples.

It's verboten at all fairs to make an offer to multiple candidates simultaneously. I've only seen it happen once, years back, and that school was banned from the fair for at least 5 years.

The director's excuse doesn't hold up. He's under no obligation to go to the fair. Recruiters regularly change their fair plans if they have filled all positions (cancelling fairs) or still have openings (adding fairs). I've known a dubious one or two to even attend a fair after they had filled all positions, though for the life of me I can't imagine doing this.

Advice from the others is spot on. If the school really wanted you, they would have offered on the spot. They're still looking and will hire someone else if they find them. Quite possibly this is due to the situation with not having a spot for your spouse, meaning you really are the number one pick, but they aren't convinced it's a good idea to hire you not knowing what to do with her. Fair enough. Would you really be happy long term, and could you really afford to stay if only one was working?

Anyway, go to Cambridge, and good luck.

I don't see the catch as a catch at all. Most MEd programs, done part-time, would take about the same amount of time to complete, and they wouldn't have the advantage of coming to your door and being subsidized.

But you do need to make sure that this MEd makes sense for you. How does it align with your career plans? Do you need an MEd that will prepare you for admin, or one that will make you a better teacher or teacher leader? What's your preferred work style? Would you prefer an on-line MEd program, which would allow you to spread out each course over a term, or what this one presumably does, which is typically compressing a course over a week to 10 days, so you'd either be meeting 4-5 hours a night after school, or having full-time classes during school holidays. So you need to know your style and whether you would flourish in this sort of set-up.

Are the programs useful? Generally yes. You can learn a lot, improve your career path and probably get a raise.

It would depend what the job is, at least if my school were looking at it. If you're teaching your own classes, etc, that would count. If you're doing some of the other things, like advising other teachers or pseudo-admin stuff, it might not count depending on what job you'd be applying for with us.

Some of those UAE public school jobs are worthwhile career-wise. Others are well-paid nonsense.

They are all part of Qatar Foundation so would offer the same package and benefits.
Awsaj is a special needs school with very scripted lesson plans.
QA Al Wakra is a new bilingual school which is still establishing itself.
QA Doha is the oldest and most established of these schools. It has an excellent reputation. It is a full IB school at all grade levels.
All serve populations which are mostly Arab.

Americans should do fine at any of them. I'm not sure what the question is really looking for. Awsaj has almost all US teachers so far. The other schools have more of an international mix, including a good dose of Americans.

QA Al Wakra is not in Doha (stating the obvious). You would probably be housed in Wakra, which is not everyone's cup of tea. It's a smaller town with limited access to entertainment and diversions. Doha is about a 30 minute drive, so not really a problem if you're used to US style commutes.