Given that Ops DH knew she didnt have keys, it is very controlling not to leave any. Whatever the reason for her not having them with her, he was a complete arse not to leave hers somewhere.
You are making the assumption that her DH knew that as a fact, when he may have just overlooked them while getting his own stuff ready for the trip and not noticed they were still in the house. If he didn't know they had been left how can he ensure they were accessible?
When I was still married to my Ex we might leave our keys at home if we were just nipping to the shop/picking DD up from school or whatever but any kind of longer/overnight trip we always took our keys just in case of emergency/the other not being in when we got home. It would never occur to me that my Ex went out without his keys for an overnight trip, and if he did then he'd probably have messaged to check they were at home and he'd not lost them somewhere when he noticed he didn't have them.
And Ops DH saying, see you tomorrow, when he knew full well he wouldn't, I am sorry, but I wouldnt put up with such lack of respect from my DH.
Again, you don't know that. Perhaps he had assumed she'd be back early and/or that his flight was later than it was so he'd have chance to see her and explain before he left, but then plans changed? So he fully expected to see her the following day but then due to the circumstances he couldn't. There's plenty of times I've said "See you tomorrow/at six" and meant it ... but before tomorrow/six has come around, something else has come up and I haven't made it, not for lack of trying.
I can see it being perfectly feasable that he thought "Right, she should be home by 10ish, I can explain/apologise and then be out of the door to be at the airport by 12 in plenty of time for the flight" unfortunately when OP didn't return at the time he tried to message her, with the idea that speaking on the phone would be the next best thing to face to face ... but the OP had no phone signal and didn't get the message until later. By this point the DH has no alternative but to leave a message as he could not call and his texts were either going unanswered or were not getting through and he needed to let her know he would be gone.
He is not a totally innocent party in this, as he should definitely be communicating his schedule better generally, but in this instance there has been issues on both sides that has contributed to the general miscommunication on this occasion, and OP doesn't seem to be acknowledging that she should take any kind of responsibility for her part in it's making.