S.S.
Hi L.,
I'm certain that this situation cannot be fun! I had a nephew that had serious behavior issues when he was little. I think he got kicked out of 4 or 5 pre-schools for biting and hitting. I have a background in Speech Pathology and Audiology and recommended that my nephew have his hearing checked. The tests showed a very moderate hearing loss and the aggression had to do with an inability to communicate. So, make sure you explore any biological reasons for the aggression as well as behavioral.
Also, as a parent of a very active little boy, who was twice as active as a toddler, I suggest you tell your son the rules of play and expected behavior and the consequences of such behavior. At age 3 he should be able to understand. And stick to the rules and consequences. Be consistent. I know that this will be an inconvenience at first, because you will just get to the park and within 5 minutes have to turn around and leave. But it should work if you're consistent.
Also, the school teachers may not see the aggressive behavior because they have other kids they're watching.
Lastly, there will always be other mothers who say nasty things about other children and their parents. It's embarrassing at the time, but give it time. They'll have their own issues with their children and hopefully you'll be more compassionate.
Good Luck!