Some cultures emphasize that all adults can discipline all children at all times, because it encourages a more communal environment and it also teaches children to respect all adults, not just the parents. Raising your voice to speak firmly is not necessarily yelling, and there is nothing wrong with being upset or expressing anger. We all feel anger.
Perhaps the only thing I would have done differently in this situation is that I might have tried to instruct the boy that "We're okay if you want to try out the car, as long as you ask us and your mommy first." Granted, the boy had no caregiver in sight and I don't know if this goes against your reasons for "not sharing." Whenever my son gets upset because another kid at the park tries to take his toys, I usually try to mediate by first suggesting to my son that he share, and then turning to the other kid and saying "we don't mind sharing if you ask."
I started doing this with my son as soon as he learned to talk. Obviously, the goal is long term and similar to your desire to have your son "stand up" for himself.
I think it was okay for you to step in. Do not feel defeated that you had to. It is a lot to ask a 5 1/2 year old to be persistent in this, but I think it is important that you have a conversation with your son about the incident if you have any lingering regrets. You don't have to be judgmental about what happened, just ask him what he thinks and tell him how you feel and then maybe discuss with him how you can both do things better next time.
As for the other mother...unless you personally know the woman and can speak with her privately about this ultra-aggressive child, I don't think there is much you can do. I suppose the only thing I would consider doing differently is take a pause before speaking to the mom next time, and see if she opens with any questions or remarks first. By the tone of her voice, you may be able to gauge whether or not it is worthwhile to have a more constructive conversation with her. If she is already defensive and huffy, then I think your response is merited. By speaking first, you gave her no option to apologize first or to engage you in a friendly manner.
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As a side story, I was at the park with my son a few months ago. He was playing with another little girl who had brought her bike (really small for preschoolers). I was chatting with her nanny a few feet from the kids when I noticed a teenager trying to ride off on the bike across the street. He had 3 friends watching and laughing at this ridiculous sight. I brought the nanny's attention to it and she quickly went over to address the situation as I stayed by the kids. I heard a "Oh, I didn't realize this bike belonged to anyone."
Right, because you didn't notice us 20 feet across the park and bikes just miraculously appear for your enjoyment from the sky.
I think kids, no matter how young, need instruction on properly asking to use other people's things. Assuming they can't or won't understand is a complete underestimation of how much children can and will understand with proper instruction.
That teenager probably lacked some instruction in his earlier years.
Keep on chugging, mama.