I couldn't bring myself to read the other responses because I know that this is something many moms have a strong feeling about, so I'll just put in my 2 cents and you'll have to sort it all out...
You have to decide what kind of mommy you want to be. I know of moms who are very big on letting kids work things out on their own and think they'll turn their child into a "momma's boy" if they step in to help out. I also know moms who think it isn't their place to say anything to anyone else's child and would rather scoop their child up and leave than speak to another person's child. I wholeheartedly disagree with that type of parenting for myself and my children. I believe with all of my heart that it takes a village to raise kids. Here is not only what I would have done, but what I HAVE done in similar situations:
Always start with the child. I don't care if the mom is right there 2 feet away watching or no where in sight--- I speak to the child first. I nicely tell them that other children would like a turn and see where it goes from there. Occasionally, they are shocked that an adult actually called them out on being mean (because obviously they usually get away with it) and they back down... sometimes they don't care what I say because they are so used to getting their own way. In that case, I instruct them on what they are expected to do in polite society where we all share this planet together-- in your case, I would have told her she can push the button one more time and then it's my son's turn. If she doesn't listen at all, and especially if she gets physical with my child, I go to mom. When you approach mom, be careful to stick to the facts instead of attacking her parenting (or lack thereof). Let mom know that she is not only not letting the other kids have a turn, but that she is pushing/hitting them.
I actually have a hard time not going ballistic on kids who think it;s OK to push other kids...but yes, it's part of being a toddler. They aren't exactly sure how to use their words yet, and some are barely talking much at that age. So how else are they going to learn to properly interact if no one is teaching them? When I was a first time mom, I couldn't understand how any parents could possibly let their child beyond arm's length on a playground... but by child #3, I realized that it's OK to let them play while you keep one eye on them and the other on a friend you are chatting with, or a magazine, or some fresh air, or whatever... So sometimes as a mom you really don't catch every little thing your child is doing. So once you've tried nicely to deal with a mean child, gently cluing mom in on what's going on is always OK. Any mom who is a witch toward you for pointing out that her child is being mean is someone you should pray for because she has an awful lot of stress in her life, and no wonder her child acts like a brat! In those rare cases, it's best to leave the playground or in the least keep a close eye on that child because she WILL strike again!
But wait! There's more!! Just as it's important to take time to help teach other children it's not OK to hit and they have to share, it's just as important for you to teach your son what HE should do in those cases. Teach him to say, "My turn?" or "Can I have a turn?" (depending on how well he speaks). Literally walk him over to the girl and say, "Joey, ask the girl if you can have a turn." When your son walked up and started to push the button, in a toddler's world everything belongs to them so she felt like other kids were touching HER toy. If he asks for a turn, low and behold she may grant him actual permission to touch "her" toy. (And if she says no after he asks, you tell her Yes, he CAN have a turn) Also, when someone hits or pushes, teach your son to use his words. Again, depending on how much he is talking, say, "Joey, tell the girl 'I don't like it when you push me' " (Or "No pushing!") You said he looked at you for guidance, so be sure to teach him what to say and do so he can defend himself without using his hands to push back.