Hello my friend. You are very correct in that your sons need therapy. SInce you are unable to pay for such outside expensive therapy, see if the children's school has a psychologist or a social worker that can assist the boys for FREE for the time being. You have done ever thing correctly and you continue to be headed in the right direction. I applaud you for being the loving and supportive parent that you seem to be. Your younger son may need a further evaluation for his ADHD and possible medication to control his implosive behavior if it seems to be worsening. For the time being, try to focus of in the positive things that your children are doing. When you discipline, the main goal is to teach right from wrong behavior through rewards, encouragement, talking, listening. respecting, and understanding. Reduce the yelling because you need to save your sanity as the single mom. REALLy praise your boys when they are behaving well. Of course still discipline them when they are disobedient but teach them what is acceptable and what us not. They need to be trained to obey with precise instructions. Set limits and correct misbehavior. Make sure that they feel loved and secure. They need to develop greater self confidence and control their impulsive behavior.
If you need more advice, just ask.