oh wow. There is a lot on your plate right now, between an almost four year old and 2 year old twins, loss of a partner to parent 4 yo, and planning on going to school full-time. Hugs to you.
Ok, as to your four year old, I love the Omega 3 and Vit. D idea. The more I read about functional nutrition, the more of a fan I am. Hopefully some supplements will make a difference. I've recently started with chia seeds which are an incredible source of Omega 3, a complete protein and have a great number of other important nutrients, which might be a good source because you're vegan.
it's hard to know how I would handle the situation, but I had a sort of similar situation:
When my second oldest son (who is 17 months younger than his older brother) would exhibit aggressive behavior like this, I would immediately separate him from the scene and make it a BIIIIIG deal. I'm generally a pretty easy going mom, so when I would act very upset it really made an impact. I'd take him in his room and tell him, "Sweetie. I know that you are a wonderful boy who would never want to hurt your brother normally. So now that you are trying to hurt him, I know that something is wrong. What is it? What would make you act so horribly to him? ( I would demonize the behavior while taking pains not to demonize the boy) I'm here. Let me help you." Then he would be angry, crying, trying to hit me. I'd hold him in my lap, so he couldn't hurt me or run away until he started to calm down. Usually took a few minutes. then he would be sad instead of angry and willing to talk to me. I'd encourage him to verbalize his feelings...what is it that makes you do something that you know is wrong? were you feeling angry, jealous, mad? etc.
I know it sounds like a lot of work but for me I was able to do it because he was the younger brother. I don't know if you could modify so that you are in the same room to keep an eye on the twins but remove 4 yo from the situation.
the basics then to sum this all up:
1. immediately and with great drama respond to ANY violent behavior
2. make it abundantly clear that we NEVER hurt anyone let alone our brothers
3. if you can remove him from the situation, it seems to make more of an impact
4. don't allow him to run away from you or hit you
5. demonize (i wish i could think of a better word but you get the idea) the behavior BUT not the boy...so you show that you know he's a good loving boy but that something must be wrong for him to act so inappropriately
6. explain how, why, his brothers must feel that their big brother who they look up to and trust and would never hurt him feel when he hurts them
7. Hold him and give him an outpouring of love while he processes his anger
8. Give him words to describe the feelings
9. give him alternate behaviors to do when he feels like he wants to hit
I don't know if anything I'm saying sparks anything for you, but I hope at least something helps.
oh and FWIW, my younger son is now 14 and is extremely good at verbalizing is feelings and asking for help. He still remembers those times when we had our 'hugs on the bed' and laughs about it now.