Hitting/Pulling Hair....Help!!

Hi everyone.
I've been doing my home daycare now for 3 months. My 21 month old daughter seems to love when the daycare kids are here. She knows their names, talks about them in the evenings and weekends and usually plays quite well with all of them. My daughter has made it a horrible habit to hit, pull hair, or push the daycare kids (usually the two oldest-one is her age and the other is 2.5years old). Most of the time the other kids do nothing to make her want to do this...she will just randomly do this...and it's getting out of hand!
I've been putting her in "time out"-telling her that "whatever" is NOT okay, it hurts and she needs to have a time out. (I have to put her on a kitchen chair to make her stay-if I sit her in the corner or on anything low like the bottom step she will just get up and it becomes a game). Once her time is up I go to her and get down to her level, tell her firmly that "whatever" hurts and it is NOT OK!. She goes to say sorry to the child she hurt. Often she will go back to the child and hurt them again!! Right in front of me!! Right after she was just in Time out for the same behavior!!
I emailed a local "tv nanny" for advice and she said to continue what I'm doing but before putting my daughter in time out, when she hurts a child, go to the child and dramatically comfort the child first and once that its been clear that the child gets the attention first, then turn to my daughter and carry out with the time out thing. I have tried this and it really hasn't helped much.
I must say that the group of daycare kids I have are generally well behaved. The 2.5 year old girl will take toys from the other children when they are playing but that's the worst behavior I have seen. No one pulls hair, bites, pushes, hits, etc...JUST MY DAUGHTER...GRRRR!!!!
Sometimes her behavior has been so out of hand that I've put her upstairs in her crib and often she will fall asleep. I don't like doing this though because it screws up her routine and I don't want her to sleep too long or else she won't nap in the afternoon or go to bed at 7pm)
This behavior is worse when my daughter is tired (but she is sleeping from 7pm-8:20am) so I don't know what to do!!
Please help!!
Thanks

[MichellesKiddos]

My 23 mo dcs was the EXACT same way. We had already done the time-out battle though (repeatedly taking him back to timeout each time he got out) so now he stays in the normal time-out spot. Don't worry, it does get better! Although at the time I didn't think it ever would haha! Every now and then he will still exhibit the same behaviors but it has drastically decreased. I would just keep doing the same thing you are doing and eventually it will pay off. With my son, I noticed that he would start pushing/hitting/biting more if he got too overstimulated with the 'daycare scene' and I would take him to his bed and give him a few toys to play with for a little while to let him calm down a bit. I've been in your boat, and some days still am, so I know it's very frustrating and sometimes disheartening when your child acts this way. One thing I read an article about, was that it's normal for young toddlers to act this way because they don't know how to express themselves in any other way. Keep things consistent and hopefully soon it will pay off for you!