No, you do not have the right to do anything. She would have probably turned her anger onto you, attacked you and claimed you were trying to kidnap the child.
You don't know the back story but obviously she was overreacting. I never use language like that to my kids but I can tell you that my 3 year old has gotten out in traffic because he got too far away from me. One of the times he has been in danger was at McDonalds. He got away from me in the playground area, ran full speed to the front door, and some kindly person opened the glass door and let him out into the parking lot. A mail carrier just barely missed running over him.
We live close to a main highway through our town and I have nightmares about him getting out at night and wandering into traffic. So I can tell you I am VERY diligent when outside that he stays within reach. Plus I am overweight and have staples in my knees from softball injuries in college and can't run fast.
If I feared he would get away and I had no one else with me that could catch him, such as another child, I would totally freak if he was getting away from me. I don't go to parks for this very reason. I think she was not being good to her child but if he was one of those who tend to run off and get in danger then she can't let up even if no cars are around,. Kids don't understand when rules ore one way at some places and then other ways somewhere else. On any other day there may be tons of cars there and she has to keep him on a short "leash" so to speak.
I feel your pain, and know it could have been me overreacting (without the bad language and rough handling) but I would probably scooped mine up and left too if he wasn't staying within the boundaries he was supposed to stay in. I would rather have a child having a temper tantrum than possible a hurt child that didn't listen when I said stop.