Help, need advice!

KP • Mama of two DD 04/14 and DS 03/16. #3 and last due 3/19
My 16 month old daughter is a bully and I don't know what to do! I'm a sahm and she is my only child but I work part time at a gym daycare. She is a bully to the other kids. Especially kids about her same age. She hits, pushes, and yells at them. Idk what to do! I don't want to resort to spanking, I don't think it will help her. I've tried taking her out of the situation , holding her hands down and telling her we don't hit and looking in her eyes. But she wiggles and gets angry and has a tantrum. Timeout is hard at the gym, really no place to out her and I have about 10 other kids to watch. Otherwise she is very sweet and loving but a terror at other times. I'm pg with #2 and don't want her to act this way to her new sibling when they come. So frustrated and embarrassed.