I'm not sure what this is in reference to, but the other mom doesn't have to get into any reasons for not letting OP's ds come over. She doesn't have to get into them with anybody.
The OP is making plans. She already said that her son won't be left alone again this summer. But, it is NOT all on the OP. If the other mom doesn't wnat to enforce her own rules, then she shouldn't bother having them. Her behaviour was ridiculously rude. Chlidren sometimes don't listen. That's a fact of life. If the other mom isn't prepared to say, "no - you can't come over", then she shouldn't have a rule saying he can't come over.
Okay - so the other mom can't force the OP to keep her child away, either.
The other mom created the entire situation, aside from the fact that OP's ds disobeyed her, which she's already addressed with him. She wants the OP to enforce her rules, but she doesn't want to enforce them herself. Ridiculous.
As to the entire thought of "well, she already had the one - she really couldn't say no to the sibling". How on earth does that follow? DD1 is frequently invited over to people's houses, and ds2 sometimes asks if he can come, too...and the answer is frequently "no". So, he has a meltdown (or doesn't, if we're lucky) and that's that. It's not the other parent's job t parent my child, so they aren't required to work things out between my children. Their job is to be the gatekeeper for their own home/children.
You continue to argue that the other mom shouldn't have to parent OP's ds, but continue to defend her decision to do so, in lieu of enforcing her own rule. Her actions make no sense.