To answer your question, yes, it is OK to tell other people/kids what YOUR rules are.
For toddlers/moms, I would suggest, telling the baby (mom to listen in)if the mother is not doing her job: "You can play if you do not push, or share, or take turns, or whatever... sometimes you need to demonstrate (point to a toy and say "may I have it now, please") please go talk to your mommy about how you going to play with "X"(your son's name) and come and tell me. The other mom will be forced to follow up and get the promise out of the kid. If there is no cooperation- you'd have to say "good - by", I am sorry.
I had friend with her kids come to our pool in the summer and the kids started splashing each other and their mother in her face in my pool. My 4 y/o froze! It was beyond offensive and improper for him. She was wincing, turning away, bagging them to stop, threatening them - nothing helped. I observed this for about a minute and to save this date and establish ground rules I firmly stated "There is no splashing in our pool. My son chimed in "Yes!"" The boy looked at me and splashed at his mom. She whined "I am so sorry". I said, "No, I am very sorry", I looked him in the eye and said: " If you splash one more time you are going home, I am sorry if you decide to spoil this date and to go home so early without eating, and playing bingo, and getting all the treats". Surprise! He got that message. Mom later told me: "Thank you, I do not know what to do with them sometimes".
I always set the boundaries with other kids and teach my kids how to do it and I know that world is big and there are many more kids/moms to be friends with in case some relationships do not work out.
Good luck.