Bluefairy, let me throw this out there, just by way of speculation. You ask, how could he do this especially at a time when you are so under stress. Well, sometimes guys do this out of boredom or because some woman is "easy" and throws herself at them, that does happen. This has nothing to do with you, it's would be about him and how susceptible he might be to that kind of lure. When it comes down to it, all marriages have problems and pressures and fights - it's one thing to jump into bed with someone, as bad as I think that is, that's usually pretty finite. It's another to have a relationship with them and to know your wife suspects or knows and to deliberately hide it and gaslight her. I'm wondering if he might be jealous or resentful at some level of the time and attention that you have to spend on your sick son. I know that sounds crazy, but my father was jealous of the family....cat. He actually go to the point where he would throw knives at the poor cat because my mother fussed over it so much. Fortunately the cat was pretty quick, as they are. He was also jealous of the ice man (and every other guy) but he didn't throw knives at him! That IS extreme and he had a lot of obvious problems, but some guys just have a problem with jealousy or sharing attention etc, and it could be a factor. So some predator makes a fuss over him, makes him feel important, talks about fun stuff with him, no stress, no problems....and it's off to the races.
So this might also involve how much attention you have to pay to your son and maybe other issues. You might consider having a talk with him about this issue, if he feels he is not getting enough attention or if you two need to spend more quality time together if it's possible. How is your son doing? Could someone else maybe handle him for a date night?
I'm obviously not excusing your husband's behavior at all, and frankly, I would still keep an eye on this because he might take it to another level. Trust your gut and keep an eye out for unusual behavior from him. But I'm just posing an idea that might give you some insight. It might not be true at all, but you'd be surprised at how jealous - not sexually jealous but just about not getting attention or being fussed over - some guys will get. A lot of the allure of the "other woman" is that she fusses over her prey, makes him feel special, things maybe you haven't had the time or energy to do. If this is an issue, maybe it would help to put it out into the open.