When your son bites, he should be placed in a time out area (preferably a chair) immediately, for approximately 5 minutes. Then, he should play by himself for a while (approximately 30 minutes). He should be allowed to play with only one other child at a time, closely supervised. Yelling at him, biting him, etc. will not have any impact. The behavior needs to be managed on the spot. In addition, even at his young age, he should be evaluated by a developmental pediatrician or developmental specialist to ascertain his developmental status and to investigate if some developmental disorder is present.
my son has just turned three and in september he was expelled from nursery in January as he bit 7 children in 11 days. Unlike your son he didnt start in daycare until he was 2 and he was okay for a few weeks, but then started throwing lots of tantrums. He then progressed to biting/ hitting the other children and eventually he started behaving like this at home. I had no idea what to do. I contacted the health visitor and he is currently being assessed. Me and his dad are seeing a community team who deal with children who are having behaviour/ emotional problems and I am hoping that we can learn to avoid situations where he resorts to biting. I recommend that you consult a professional if you can. Even if there is no physical problem you need support. I hope that you find a solution to your problem. One thing about my son is that he behaves much worse around me and I realised recently that because I feel guilty about leaving him with others in the day I tend to let him 'dominate' me :i.e. if he threw toys in a tantrum I would give them back,and if he threw a tantrum when I came to collect him I would spend ages unsuccesfully trying to coax him to come and then end up frustrated and angry myself. Recently when I came to collect him he came up and hit me and told me to go away, so I said 'okay' and got in the car. When I did this he realised I wasnt going to put up with his tantrum and he started to cry. I got back out of the car and asked him to come home with me. He came with me and was laughing and happy all the way home, and picking him up hasnt been as bad since (fantastic as it really upset me and him the way it was before). I hope this helps.
That's an excellent point about your son 'dominating' you, I believe the same thing may be playing out with my 2 1/2 year old boy. He's a hitter and I'm at my wits end with him also, I just found out that at the babysitter's he's hitting her one year old son. I know consistency is the key but consistently do what? Yell at him? Hit him? Time out? I'm at my wits end also, I have noticed that if I do stick to one thing consistently like not letting him on the back stairs he loses interest in it.
A related discussion, Toddler Biting