Helping DD managing friendship issue

[bigbassdrumbanger]

Dd(11) has just started secondary. She's always had friends, but never had a best friend, and is not one of the popular It-girl types (as she would call them).
On Thursdays she goes to a local club after school. A friend comes home with her, they get changed and walk there together. Past couple of weeks another (quite loud) girl, who was in dds primary school friendship group has come along too. Dd finds this girl a bit full on, so when she asked dd if she could come back last time, dd said no. The girl apparently wouldn't take no for an answer, and came to my house with dd and other girl anyway. They were only here for about 10mins, but within that time, she managed to piss Dd off by pulling toys and things out of her drawers, scraping the surface off one of her squishies, being generally loud and irritating. Dd was quite angry and very upset, but seems to feel powerless as the girl ignored her when she said not to come round.
I've told Dd that she's entitled to say no to this girl, but I'm not sure she feels able to manage the situation - I want to help her, but I'm not sure the extent to which I should get involved. Do I contact the girls mum about it, or do I speak to the girl if she arrives back here this Thursday.
I'd love Dd to feel empowered to deal with this herself, but she seems to be finding it overwhelming, and I'm worried that she might get angry and lash out at the other girl, as she seems to be lacking the tools to manage it assertively.
How would anyone else deal with this situation?

If she turns up next time just ask say something like "oh I didn't think you were invited "susan", dd did you invited "susan back?" That gives your dd a chance to say no hopefully and you can kindly and sweetly say to "Susan" or whatever her name is "nice of you to pop by, maybe we'll see you another day, bye!" Sounds cruel but she needs to learn bounderies and that she can't just bully her way into someone else's home.

Would your DD be okay saying "my mum will only let me have one friend back"? It has more authority if it sounds like it's from a parent so might work.

A combination of those 2 approaches might be sensible. I really want to teach Dd that no is a one word answer, she doesn't have to explain herself! But I suppose sometimes life can be a bit more complicated than that, and some people are just harder to manage than others.

Let us know how it goes! Probably Thursday will come and nothing will happen!