Sometimes, or quite often, it might be not about their struggles with "education", but about their struggles with a combination of unfortunate circumstances, such as not the best classroom teacher (this is a very strong factor!), bullying by some of the classmates (your kid might be silent about it), some embarrassing episode at school that hurt your kid deeply, etc. It sounds like one of your sons, who refuses to go to school, has more reasons for that behavior than just his lamentations over the end of the summer. It looks like something or somebody makes his experience at school very uncomfortable, or maybe even painful. It might be helpful to talk to the classroom teacher, and/or try to figure out if you son has any friends in his class, etc. I guess you are already doing these things as you are saying "I am trying to get to the bottom of what is going on with him". Of course it is very important that he feels your support. Hope your attention, patience and persistence will help you to find the reasons for his so strong refusal to go to school, and to address them.
And of course the same recipe, - attention, patience and persistence, - will certainly help the other son with the suspected ADHD. It is very, very difficult to handle these things alone, especially for a working mom. It looks like you are doing a great job supporting your boys in their struggles at school. Love conquers everything; you will get through it, Juliette. And your sons will:-)