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!