It sounds to me like your family is in great need of family therapy. At the age of 13 kids are not quite mature enough to process serious situations like your family is facing in the same way an adult would. It is difficult for teenagers to be respectful even when their family is not facing emotionally traumatic situations.
As an adult and the spouse in your situation, it is perfectly fine for you to choose to overlook your wife's indiscretion if thats what you want to do. However, you can't ignore the pain and confusion it has caused your son. As he ages and understands more and more firmly develops his sense of right and wrong, actions and consequences, it will become even more important. She didn't just sin against you and your marriage, she also sinned against your whole family, including your son.
Now, on top of having to deal with his mother's poor choice, and your silence on the matter, he has to face the fact that his mother has a serious, chronic illness that is affecting everything in your home and every relationship in the family.
IMO, he has a right to be angry. Should he be disrespectful? No. But he is a kid. That's what they do. His disrespect is harming your wife? So. She has to make amends ...not just with you, but your whole family, before he can have a right relationship with her. She is sick now, but that does not undo the damage she caused, which was very real. She caused this. She has to take an active role in correcting and bringing about healing for your family.
Stuff your feelings about your wife's affair all you want, but your son is hurting, and you are doing nothing about it while demanding respect from him. I call foul.
How did she have sex on school property and not get arrested?