First if he is at your house or in the park with you, then by all means treat him as you would yours. IN other words he is 3, he pushes on the slide, he gets 3 minutes time out.
Even now I tell my friends that if my kids act up to punish them as they would their own. My kids have come home and said "Ms. Jeanie" put us all in time out. I say good for Ms Jeanie, mind your manners at her house. Mine are older, preteens and teens.
Tell the mom, be up front. 3 yo's push and hit and need to know where the boundaries are. Ask her what her consequences would be and tell her that you would absolutely want her to discipline your child if he were to act up at her house.
She should understand.
I would also tell the teacher, just as an FYI. Not as a Guess what Johnny is doing to my Sammy. Just let her know Johnny has been kind of aggressive to Sammy and you were wondering if he were acting that way at school.
And as a mom of a formerly agressive child, please invite the child back to your house and be sure to let him know the rules and consequences. .