Hi and welcome, The best way to entertain your girlfriend is for the two of you to go away for the night. There are no "rules", you have to look at your own situation and decide. If your daughter knows your girlfriend and has spent time with her before it probably wouldn't be a big deal for her to stay. If this is a new friend I would not advise it, it's too transient..
Hi, different spin on your question. You did nothing wrong, in fact you did all the right things. Your ex is angry and this is a pretty common situation to be in after a split up. Don't engage her in an argument over it. Just simply state that you know what is right and wrong, and you had your daughter's presence in mind when you made the plans. Life goes on after divorce.