M.G.
I agree with Diane. Some can be just typical 2 year old behavior (being disagreeable and testing his limits with his behavior) but I would think he's just reacting to the upsets in his life.
Is anyone talking to him, and explaining what's going on? Listening to him? Quiet time?
I was ill for a long while and my kids really reacted. One quite badly. A lot of one on one time was required - just laying on the floor, playing Lego, or reading. Sometimes just walks. Does he just spend time with his mom without anyone around? (without baby?). He may be very needy at this point - emotionally.
As for the food - throwing it and such, some of that is typical (a phase) also.
You just put out only so much at a time. If you're giving little pieces of a sandwich for example, you could do one corner of a sandwich at a time. When he's done that piece, and he's a good boy, and he wants another - he can ask nicely, you hand him the next piece. You don't want to make it a reward exactly, but reward good behavior by responding. Ignore inappropriate behavior.
Spitting, pulling hair, etc. you just calmly remove him and put him in another room where he's safe, and say "When you can behave and be kind, you may join me and we will play (lego, playdough .. whatever fun thing that he would like to do) so he gets that he cannot join you unless he behaves.
I never removed stuff like toys. I just made it CLEAR that they were not to join in unless they were well behaved. That worked far better for me.
I hope your daughter recovers soon. How terrible. How nice that you are helping out!