I notice that you said right off that your 14 year old is super smart. Is your youngest son as smart? or perhaps does he feel 'stupid or slow' because he isn't quite up to his brother's abilities? Parents have a tendendy to label their children. It happened in my own house, with my brother and me. I was the smart one and the talented one-I always got the best grades, I was given the standardized tests and got the highest grade in our state, my brother (while still above average) felt stupid and did barely enough to get by in school and compensated by being funny. I won competitions in music and dance, while he was chubby and played video games. To this day, our grandmother talks about how lazy he was all growing up and what a blessing I was. It has made him angry at me and consequently he doesn't talk to me hardly at all. This guy is head of IT now for Homeland Security for Cisco, makes a great six figure salary and so does his wife-but he still can't get over the way he was compared to his sister during childhood!
Perhaps your son is being compared to his older brother by teachers and maybe by the family. It can make him angry, have outbursts, and feel really out of sorts. He won't fit any 'profile' because he is trying to find his place within the family and society. Little things can set him off, and compliments can sometimes feel like lies...I know that sounds strange, but if he feels like he's not good enough and someone tells him he's great, he's not going to believe them-so he discounts them as being a liar.
I would find him a good child psychologist that can get him to open up and talk about his feelings. You need to go back to work, it's probably making him feel guilty that you can't work because of him. If necessary, you make him go to school and have the school provide him counseling during the day so he can have a safe environment to talk about his problems. If they won't provide that, you take it to the school board, they are required to provide counseling services for children, at least in most states. Talk to your local Social Services and see if they have counseling programs he can become involved in that will help him gain confidence outside of school. I know in our community we have 4-H and it does wonders for children in rural settings that don't get to have a lot of activities outside of school with other kids. Children need to have positive activities where they don't have to worry about 'fitting in' or how they look or being picked on. If your son is interested in sports, see about getting him in a youth league outside of school, so he doesn't have to see school coaches, but instead can be taught by parents and he can make friends that go to other schools-look at it as giving him a new start. If possible, you may want to see about changing him to another public school, even if you have to drive him to school each morning. Your oldest will be driving soon, and he can drive him then. But even if he kicks and screams, he has to get an education and he has to have some activities with other kids. He can't be allowed to hide from these problems. If you give in, he will grow up learning to not deal with people and just avoiding problems rather than facing them. Even children and adults with serious illnesses have to learn how to deal with problems in the outside world in a positive way. The world doesn't change much, we have to change our reactions to it and learn how to make negative situations have positive outcomes. When something bad happens to your son, you should let him vent his anger, then sit down and discuss how things could have been better if he had changed the way he reacted. Be careful not to make this into a 'blame session' but instead a 'what if' session, and it can be fun if you make it that way. Remember to give rewards for good behavior, and if he's had a really bad, lots of hugs can help make the bad feelings go away. And when you've had a bad day, ask him for a hug to make it go away, or if you had a good day, celebrate it with him. Parents are the best role models for children, so let him learn from YOUR behavior!
There should be a mental health facility in your county that is based on income, you can call your local hospital and ask them and they will tell you where to call. They will set your son up for an appointment, and I would ask if you could get him evaluated and if it would be possible to have family counseling as well.
This is not going to be a quick fix. It took a long time for him to develop these problems, and it's going to take even longer to get him better. The main thing is not to give up. You have to keep trying, you have to keep as positive as possible, and when he gets upset you need to comfort him and listen to what he's saying and talk to him about how you feel too. He's old enough to hear your fears and answer questions when you ask him what you can do to help him. Be honest with him, tell him you're worried but that you are going to do all you can to help him feel better. Make sure he knows that you love him, that his brother loves him, and that you're never leaving, and you're never giving up!
If you have any questions or hit any roadblocks, just write me again. I wish you all the best!