So many issues here.
When you say he knows she has anxiety, does he understand how it manifests? Would he even think that she could need to leave cinema and not come back?
My son has extreme anxiety, but often no one would know, because he doesn't have "attacks" where all reasoning goes out of their brains. It depends on whether they're a freeze or flight sort of person.
Meanwhile, I do think your reaction is OTT, and I say that as someone who spends most of her life having to suppress her inner helicopter.
Spending a day with your daughter's friend, or seeing her at home when she comes to visit is clearly not the same as going away for a couple of days and being in loco parentis.
Did you have a chat with him about potential situations? That would be the least I would expect in terms of managing expectations, and situations.
At least now you know that in your absence your daughter needs a plan b and c for if she needs to exit fast.
The WORST thing you can now do is say she will never be allowed away again.
The dad is irritating because, from very little info, he seems to have no clue as to what is involved. Even down to his text, a reasonable parent might say "sorry I didn't see this, and didn't see her leave. But she's safe now, and will keep a close eye" rather than minimising. Maybe it's not minimising if he truly doesn't get it.
I DO understand your alarm, but I truly hope your daughter has no inkling of your outrage or panic, because if she does, then you need to look at your coping mechanisms too.
If you've just vented on MN, all good.