You are right to be concerned that employers will be afraid to hire you because of your diagnosis, and an unfortunate consequence of the Americans with Disabilities Act (if you are an American) is that they will not be honest about this with you. The worst case from their viewpoint is that they hire you, find you don’t fit in, but then are told they can’t fire you because doing so would constitute discrimination. To combat this consider offering to first take a temporary part time or internship position so they can get to know you. My guess is that the first sentence of your post would greatly concern most potential employers.
I’m not sure about the timeline of your employment gap, but you might be able to use the fact that you have a special needs child as a justification for it.
There is a reasonable chance that your current employer assigns a high probability to your having autism because (a) of your behavior, (b) being told that your daughter has autism got them to think about autism and connect it with your behavior, and (c) someone realizes that your daughter having autism raises the probability that you have it.
My autistic daughter is also intellectually disabled. She needs lots of special care, often on a difficult-to-predict basis. It was especially so in the first years following her official diagnosis. Not sure if it’s a good thing to mention this, though: I’m afraid the employer could take this as evidence that there’s a significant risk that I could some day descend into a poor productivity phase (or even another leave, at no notice). It may also be the case someone could take all this as a positive, by correlating it to a potential underlying disposition or motivation to hard work and responsability, but it seems better not to count on the possibility that this effect could override the first one.
An option would be to tell employers that I was on a leave to take care of a very sick family member (say suffering from the illness I suffered from) that since then has been definitely transferred to a special care facility, while trying to “fill” the gap with some skill-sharpening/expansion activities I did during the period. Classical example being online courses directly related to my main career path. Unfortunately it was not the case, as a I took online courses on online education, while planning to apply for typical engineering jobs. It’s still something to show for that time off. I can try to make it applicable—e.g. I can relate it to being able to gain a skill to train others or take team leadership if necessary, or find ways to train people in other offices without having to travel.
Current employer is aware of my somewhat extraordinary circumstances involving both, being a father of a disabled child (my autistic daughter is also intellectually disabled and needs lots of special care, often on an unpredictable basis) and suffering from anxiety disorders myself. The employer was able to offer special working conditions regularly (e.g. working from home during a crisis).
You might want to try a mixed strategy where you reveal different information to different potential employers. Since you only want one job, you would likely gain by this variance increasing strategy.
It doesn’t sound like chemotaxis101 can easily use a mixed strategy, as he intends to publicly disclose his diagnostic status.
Note that what I’m going to diclose is the fact I have Asperger’s, rather than the underlying (unrelated) reasons for the gap in my resume.