I'm at the end of my rope. What has helped you/ your preschooler when t comes to pushing and generally being too rough?

My 3.5 yo is regularly way too rough with her 1 year old sister. Sometimes it's play that gets too crazy, which is annoying but understandable. Sometimes the baby is being annoying to her and trying to play with whatever big sis has and the big one pushes her away- not ok, but understandable at least. But sometimes they are playing really well together and out of nowhere she just pushes the baby, pretty hard. She also does it with her friends, particularly in a class they take together, usually over waiting in line and taking turns.

I really don't know what to do. I do know that my losing my temper and yelling doesn't fix it. At home we do time outs any time she is too rough but it doesn't seem to have an effect. Sometimes I just take the baby and leave whatever room she is in because she can't play nice. In her class ivemadejer leave class and sit in the waiting room for five minutes while everyone else kept having fun. But it's getting worse and I am so sick of it. I have not heard of her doing it at preschool. Yet.

Any advice? Do they make boarding schools for 3 year olds?