I went through this too with my daughter. I was at a loss so i asked for advice from a friend who did home care for years with her own kids. She pointed out that my DD was looking for attention in anyway she could get it. So we began with a conversation in the morning that if she misbehaves she will get a time out. then when she hit or pushed without saying a word i would pick her up and strap her in her highchair. I would set a timer and just say "when the timer goes off you can get out." then when the timer goes off i would take her out and not say anything but go about business. (fully aware its not the safest place incase she toppled it over but she's my own kid and it worked.)
Many people follow the steps where you talk to them after time out and say sorry and have a hug but that process didn't work. this process worked wonders took a couple days and she started to understand and it slowly tapered off. Good luck though the 2's are hard enough already!!!