Sounds like you have a strong willed child!! Plus you are running a Day Care (more than likely against his will) as far as he is concerned he would like them all to go home and have his Mommy to himself! My son had a few issues at that age, not a biter or hitter, but did get upset a bit and I could tell it was over the "child invasion". If he is 3 he is def ready for more mature discipline "what ever that is for you" but firm. Dont give in, stick to your word. (assuming he is also a bit of a manipulator) Dont treat him any dif from the daycare, as matter of fact sometimes of course (because he is your child) you can be more stearn and let him know there is no room to budge. Wow! sounds like you are having a "time", it will get better.......I believe there is more of terrible 3's rather than 2's.
What type things do you do when he bites or gets aggressive with the others?