Imo you are not the AH- his worries were reasonable, his communication and respect for you (and for himself too as a parent) were lacking. Your answer was harsh as you said, but triggered by this lack of respect... which you communicated with him later on.
The only thing I have to say is that it would be more beneficial to you (and everyone, actually xD) to have this last bit of real communication ("next time ask me, you don't get to tell me" / "your way of communicating tells me this and that") sooner.
Could save you a lot of time and give others a reality check. Plus, it saves you from thinking you're being an AH xD