My kids are the exact same ages as yours except that my oldest is a girl and my youngest a boy. My daughter pretty much followed the same pattern as your son (ignoring the baby in the beginning and then showing interest and now being more hostile). I don't know about you but I found that when I listened to myself I was constantly on my daughter to be nice to her brother. I've tried to change that by recognizing the times that he really is getting on her nerves and into her things and saying things like, "Nathan, your sister had that first. Please give it back to her," or "No, Nathan you can't have that your sister is playing with it now," or even trying to have him say thank you to her when she does something nice for him.
I've also given my daughter permission to gently push her brother's hand away if he gets into what she is playing with but not to push him hard or yell at him and that she needs to get us when he won't stop and not take it into her own hands by hitting. As far as when they start getting irrational like your son saying he won't sit in a chair or watch TV when your daughter is around I usually tell my daughter very calmly, "Nathan is allowed to watch that show also. If you don't want to watch it with him you can go somewhere else." And if she throws a fit, I put her in her room and tell her she can come out when she's done. Or at dinner, you could say, "That's fine if you're not going to sit with us. You need to go to your room instead and if you decide you'd like to eat dinner with the rest of us in your chair, you're welcome to come out." I also try to say a lot, "Don't we love Nathan?" or "Nathan, don't we just love your sister?" I hope this helps. My daughter can still be really nasty to her brother but we're making progress. Even though the behavior isn't always acceptable, it's still normal for their age. We've also had success with potty training by using a sticker chart with rewards from the dollar store and I've been thinking of trying the same thing by rewarding my daughter with anything positive at all she does with her brother. Good luck!