Wow. Just wow.
Since the other driver admitted 100% responsibility here, your Mom Boss has no right at all to criticize your driving skills. Plus, it wasn't a major collision or anything. This could have happened to anyone, including HER. Many people get involved in things like this...Even if they are paying full attention to the road.
Do not give this job more time. I would probably leave on the spot because of how the Mom Boss talked to me, but if you have to for financial reasons then you can always give notice tomorrow.
Considering it has only been a month, you won't need to use them as a reference.
Another reason I would quit is because it seems the parents are not concerned that their son disobeyed you so blatantly by leaving w/out permission. That would be a concern for me as a parent, but it sounds like they are only interested in berating your driving.
They are crazy and their logic is so flawed, I won't even get into the reason(s) why.
I am glad you + the kids were okay.
So sorry about your car.
