Not only did he assault your DD he stood in court and admitted it, for which he was found guilty and given, IMO, a paltry fine.
You're now letting this very same man spend time with her without being there?
Is there a valid reason why you're letting the very person that assaulted your DD spend time with her without you being there?
Yes, your DD's father should have stuck to the agreement but felt so cock sure of himself he over ruled you, any chance that's because he sees someone that would allow him to take the very child he assaulted out for the day as being weak.
He now wants to take her to the beach with a friend tomorrow, and she would like to go. I want to say no, and he didn't stick to the agreement today. Is this the right thing to do?
You're not wrong to stop him seeing her, but it should be because he's abused her and not because he broke the agreement.
I could, but she particularly wants to go with her friend and I can't tomorrow.
I'm assuming there wasn't any restrictions on him seeing his DD given while in court.
Are you the resident parent? If so you need to start being the resident parent where her and her father arranging outings are concerned, you either stop him taking her out, anywhere, or you don't, you can't stop him inorder to punish him as that will punish your DD too.
In this case maybe a court order for acsess would be better, then if he breaks it its not you he's going against.