I know you were worried about your daughter. Hey, I'm a mom, so no problem with understanding that.
I think that perhaps from your husband's point of view, you may have seemed to be insinuating that he wasn't capable of taking care of her.
My EX husband has taken our son to plenty of dental and medical appointments and I don't expect to hear from him while I'm at work unless something goes wrong. There's never been an emergency when my ex has taken him.
I had all four of my wisdom teeth removed at the same time and I literally woke up wondering when they were going to get started. It was already over. I didn't feel a thing. I went home and slept. It's far more taxing on the parent who has to go and wait and worry.
Just saying.......
I'm not trying to negate your feelings at all, I just think that your husband felt he was handling the situation and all went well. Now he's having a hard time understanding why you are mad at him because he didn't TELL you that he handled it and everything was okay.
If your daughter is fine and the turmoil is over, I would say to just let it go as opposed to fighting about it. You were worried and nervous. There's nothing wrong with admitting it. Beyond that, let it go this time and let him know that next time, it will calm your nerves to hear from him, even just for a second.
Let him know, for sure, that it has nothing to do with not trusting him.
Best wishes.