Thanks for writing to Just Answer.
I can understand how him referring to the girl as cute and asking about her name a couple of hours later (showing he was still thinking about her) would bother you!
Is it enough to end the relationship over? The fact that this has occurred to you is probably an indication that you have had some other doubts about this man, whether conscious or not.
If I'm wrong, and there have not been any other red flags (and I mean none) during the time you've known him, then it may be rash to end it over that statement. But having said that, I would not have him over while your children are home.
I have to admit to that my "antenna" went up as I read your note. A simple "she's cute" wouldn't be a huge cause for concern. But why would he still be thinking about her several hours later? That just seems strange, and a little creepy (not a technical term, but it fits).. He has a daughter of his own--you would think that would make him sensitive to appropriate behavior & comments.
It's almost impossible to be too careful in this day and age. And I have a feeling that this won't fade from your memory, and will keep you from feeling relaxed and secure about this man.
It may be time to move on. Better safe than having to worry about such things with a man you're dating. I've treated too many children & teens that were molested by their mother's boyfriends to think that nothing could happen.
I wish you the best,