I think it was appropriate for you to ask her to find another place. If you were a large center, then I would feel differently because you would have some resources to support you and other role models for the children.
However, I do wonder about his behavior, and maybe he needs some interventions. I would refer the mom to your city's Birth-Three program. Every state has one. It is generally run by either Health and Welfare or the school district. Basically it is like Special Education, and behavior/social skills can be specifically targeted for interventions, even if they are academically where they need to be. The program would evalutate him using a variety of assessments in the social/behvior area. If he is found to be significantly lacking the skills he should have at his age they will (most likely, as this is how it works in my state) send a child development specialist to his house to work with him and teach him the skills he needs to cope. When he turns 3 (in most states) he will be offered to attend a preschool program (if he continues to show a need). These programs are FREE - the earlier children recieve needed intervention the less they will probably need it when they go to school.
To help turn mom onto the idea of having her son evaluated, I'd find out exactly who to call and give her that specific information (your doctor office might have the info, or call Health and Welfare and/or the school district main office to find out).
Let her know it's free, he might get free preschool (that might be an incentive right there for her ) and that it should help him, so when he becomes kindergarten age he is more likely to be able to be in the classroom with his classmates, rather than be pulled out due to behaviors (and if he still has similar lack of social skills in kindergarten, he'll be evaluated for special education anyway, may as well give him a head start now so he'll need fewer, if any, interventions when he is school age.)
If mom does not want to have him evaluated, or he doesn't show enough need for support and intervention to qualify, or simply in the meantime, I would look into courses on parenting the difficult child. I really like the overall program of Love and Logic - and there are a lot of positive methods for helping to teach a child the skills they need.
Also, instead of time outs or other punative methods, I'd try more positive approaches. Before you turn on the TV, remind him he gets to watch one show then the TV will turn off, then set a timer to correspond with the end of the program so he can see how much time is left. Give him warnings towards the end of the show that it is almost time to turn off the tv. Give him the choice to turn it off himself with the remote or on the tv itself.
Basically, prepare him for what is going to happen, how he is expected to behave, acknowledge his feelings ("I know you don't like strangers here. When a stranger comes into the house, you can go play in the other room with a toy until they leave. That way you don't have to see them" - or whatever similar will work in your situation).
When he hurts your son, pull him away so he isn't able to hurt your son, but then talk with them both, figure out the situation, then have them role play (with you telling them what to say and do) a proper way to solve the situation. Ex: "You want the car that Jimmy is playing with, ask him for the car, he might say "yes" he might say "no". Say "Car please"". Then help your son respond approrpaitey "here" or "mine". Then help the daycare child by saying "you said please and he said yes! your words help!" or "He said he is playing with it, he will give it to you when he is done. It is hard to wait, but we can do it. Let's play with X while we wait" - You might need to simplfy the langauge more. If your son says no, then, at first as the daycare child is learning, convince your son to give up his toy sooner than later. That way daycare child learns that he can wait and play with something else, and then he will get what he wants. If you make him wait too long you'll get a meltdown instead of a lesson learned. When he does get the toy he wants say "Look, you waited and now you have the toy! Great Waiting!"
I hope this gives you some ideas. I really thing the child may need some sort of intervention. He may or may not have an official disability - that doesn't matter. What he needs is someone who is trained in doing what I have posted here, and more to help him learn the skills he needs. Good luck.
PS - one other incentive of getting mom to evaluate him, let her know you will only continue to sit for him if she has him evaluated by a certain date.
State Certified Early Childhood Special Education Teacher
New Mom as of March 2009!