You're not doing anything wrong. Your son is probably trying to get your attention. He has to share his momma now, and toddlers aren't known at the best of times for their sharing capabilities, especially when it comes to their parents.
I would put a pack n play in the main play area. I would put him in it for more than a minute (maybe three?) every time he offends. I would swiftly grab him, speak in your angry voice, and let him know that biting/hitting/pulling hair is NOT acceptable. Let him watch as you and the daycare kids do something fun without him. When he can see what he is missing, when he knows that you're upset, he'll get the message. Like everything with kids, consistency is paramount.
Good luck!
Don't disipline in the main area it doesn't work and it causes more aggression. No one likes being singled out infront of everyone else. Put him in his room.