How to curb pushing. How to dscipline your own kids in dc and te sibling rel.

My almost 3 y o daughter pushes her baby sister over when she is frustrated e.g. grabs her toy, interrupts her play or is generally annoying to her. I know this is developmentally appropriate but I am wondering what I can do to help curb the behaviour. The sibling dynamic is at play here but I also wonder if she or one of the other dck would do this to another "annoying baby" that joined our group.

So currently I am placing her on time out and I am coaching her to take a deep breath before reacting and ask mommy for help. I really coach all the kids to "use your words" when frustrated and I have seen great improvements in this area. Even seeing them coach each other to "tell her you don't like it."

I guess my question is about disciplining your own kids in dc. Another dck would respond to a time out, apologize and move on. My daughter normally responds to time outs but in the daycare setting less so. I feel I have to keep "upping the ante" so to speak and use stronger consequences since I can e.g. send her upstairs away from the other kids, remove evening privileges. These things I would obviously never do with a dkc child as I couldn't follow them up etc. I feel like I am being harder on my own kid and I don't like it, however she is challenging me more than usual in the dc. She also isn't getting her afternoon nap since the dc started. She just stares at the ceiling and this is definitely contributing to the problem. I keep debating having her nap in her room (she wants to nap with the other kids) and I tried this once but it was a lot more difficult as she remained in her bed and wouldn't come down for the school pick up (had to leave the other kids go up and carry her down, put on her snow pants etc so we could leave). I think once I am done with b&a things will greatly improved.

Any suggestions?

I think you are on the right track. Our own kids can definitely be the ones who challenge us the most!!
My youngest is the daycare bully right now. She is one and a half, and has decided to mark her territory by being aggressive. I react EXACTLY the same with consequences, as I would another dck.
Jut be patient and consistent, and it will get better!!