American Teacher wanting to teach in Glasgow, Scotland.

You would need need to find a job, and then get a work permit in that order.
Your qualifications may or may not be recognised in the UK. "Illinois Teaching License", "Special Education K-12" and "Elementary Education K-9" are meaningless terms in the UK, what is K-12 and K-9?
You then need to find an employer who wants you, and can state that he cannot find a suitable employee who is an EU citizen. Then the employer has to apply for the work permit for you.

I suggest you ask your boyfriend to do some research locally about potential employers. it would be easier for him than for you to do this remotely.

Of course you could just come to visit your boyfriend as a tourist, but if airport immigration thinks you are coming to stay permanently (no return flight), or to look for a job they could refuse you entry at the airport and send you back on the next flight.

Sorry if I sound negative, I am just trying to be realistic.

If you have a University / College recognized teaching qualification and current State Certification then you will probably meet the requirement to teach in Scotland, but each case is considered individually by the GTCS, even for people with English qualifications.

Although there is in general somewhat of a shortage of special needs teachers in the UK there is at present no inclusion on the shortage occupation list for a visa, as there is for maths and physics teachers.

This does not mean you can't get entry but it will probably be more difficult for the sponsoring employer if you can find one and more expensive for you.

The first two posts summarize your challenges quite succinctly. There are many legal barriers to foreigners living or working in the UK, as in the USA, and therefore no agency to facilitate the plan.

Just wondering ... are the rules for a "spouse" different than rules for a legally unrelated person ?

Oh yes. If you were a spouse, and your hubby is an EU citizen or a legal resident in the UK with a work permit, than you would be able to get a visa to join him and work in the UK. As would your children.
The normal situation is when your spouse applied for his residence and work permit (officially called an "Indefinite leave to remain", the equivalent of a US "green card"), he would add you as a dependant.

But, if you get married now, it rings alarm bells about "sham marriages". There is a catch 22 here. The test they apply is "did you get married purely for the purposes of gaining entry to the UK". This is designed to catch people who don't know each other and are paid to do false marriages. But, if you are a legitimate couple who have been happily living together for years, and probably would carry on doing so for the rest of their lives if they didn't want to move to the UK, then the answers also "yes", but they are actually legit.

If you try to marry after your partner is already in the UK, expect lots of questions, suspicion, delay and bureaucracy before you are allowed to join him.

He was born and raised in the UK but I am in no rush to marry. We met while he was working abroad in America and would like to live in the same country. He is also looking at jobs in the U.S. but it is also quite hard to get a work VISA here as well.