Whew! you certainly have a full time job! Well two full time jobs! I admire single parents and wish you good luck.
I think a chat with the teachers in your children's life would be beneficial. I tease my husband sometimes about how awful our kids will behave around us when they are 'little angels' when visiting their aunt's house or their grandmothers house! The school teachers can give you an idea of how introverted or extroverted they seem, how much difficulty, if any, they have with making friends or with understanding when a joke is made. One of the key things to look for regarding Asperger's is lack of social skills. Being able to tell a tense, forced smile is different from a relaxed, easy smile and that the former might mean your peer isn't joking!
I'm blessed with a marriage with a very wonderful husband and father. We will soon celebrate our 19th anniversary. We have three sons, now of the ages 15, 10 and 7.
My 15-yr-old (diagnosed with Asperger's) is a sophomore in high school. He shows great respect for his elders and teachers (adults in general). He has a difficult time making a friend and difficulty keeping a friend. His idea of "fitting in" is talking about non-personal things, such as Pokemon or Bakugan. If a peer doesn't want to talk about my son's favorite subject (his interest of the day), he looks for someone else. There was a time, around 5th grade and 6th grade, when he was convinced that every one of his peers thought ill of him: he was skinny, he was the teacher's pet, he wears glasses. If he heard some whispering, he was convinced it was negative comments about himself. If someone got too close (physically), he would overreact just in defense of a perceived attack or confrontation. Another thing is he couldn't (it is still hard to) handle a time out if he wasn't told how long the time out would be for. There was this one time, I'm convinced, that if he had simply been told 'I'll give you 5 minutes; you need to calm down; and I'll be right back to talk to you" he wouldn't have thrown chairs and been wailing about how unfair he was being treated. (That was an 'interesting' day!)
My 10-yr-old son (also diagnosed with Asperger's) is now in 5th grade and while he can call some of his classmates friends, it isn't what I would call a friendship. He absolutely hates having his older brother tell him what he can't do. Most outstanding is his lack of understanding feeling words ("she felt shunned by her friends" or "he was devastated when his dog died"). Like his older brother, he finds himself more comfortable with adults. Uniquely, he adores babies and young children. He will want to do something that would get the baby to smile or giggle. One of the most memorable times which pertains to your question is the day he came home from school crying that his friend didn't want to play with him anymore. I asked about the situation and he finally told me that the classmate he had been playing "Pokemon" with decided he wanted to play something else. Well, my son didn't want to play 'something else' and perceived his friend as meaning he wouldn't play with my son because he didn't want to be friends anymore. This son of mine finds it very hard to let someone else decide what to play. At home, he finds it hard to end his turn on the Wii so one of his brothers can have their turn.
Another memorable thing is my second son did not have any understanding of 'stranger danger'. It was something we had to teach him. Most kids can understand without having everything spelled out.
My youngest has been diagnosed as autistic. He is high functioning and spends a good part of his school day in the "regular" classroom and not off in a small group classroom or resource class. He shares many of the same characteristics as his brothers, like misunderstanding a peer's body language.
I've had a good read from a book titled "An Oasis Guide to Asperger Syndrome". You might find it at your local public library. My husband liked reading some of it just to understand better what Asperger Syndrom is.
Good luck!