To not want this girl at dd party

[XiCi]

Dd is 9. One of her friendship group from school has been quite nasty to her online and via text during lockdown. Pressurising dd to give her her pets on Roblox, texting her and calling her a bitch when dd refused, threatening her saying her mum was going to batter her if she didnt do as she asked. After this they stopped communicating however dd sent a little text a few weeks later saying its friendship day shall we just be friends again and got a one word NO in reply. Its dds birthday next week and I'm just having a few girls over to play in the garden. This girl has found about about this and has now started texting dd asking if she can come and saying they can be friends again. Dd is a bit conflicted, she thinks she only wants to be her friend because of the party but hasnt got a nasty bone in her body and I think her default would be to just let her come. This girl is trying to video call her all the time for an invite. MIL thinks that all young girls have fallings out like this and I should just invite her. AIBU to not want this girl in my house after i saw how upset she made my dd. I dont know whether I'm just being over protective.

Noway would i invite her. If you invite her it sends your daughter a message to be a doormat and put others feelings before hers and be a people pleaser. Just no no and no!
You dont even need to say covid rules in my opinion that mean girl should be blocked.

It's absolutely no excuse for the girl's bad behaviour, but do you know anything of her background/situation at home etc?

Why I ask is that I worked for a few years at a primary PRU (pupil referral unit) and as you can imagine, some of these kids presented as really "not nice," including towards each other. However, beneath it all they were often extremely lonely. The Year 6 kids in particular were the ones who had never once been invited to a party while the rest of their (at the time mainstream) class had been and you can imagine the hurt and how it just served to reinforce the negative view they already had of themselves.

I remember one particular kid - we'd had a terrible day with her - she'd been very violent and been in holds for some of it, calling us every swear under the sun and spitting at us. When she'd finally calmed and I went over to support her with her writing she said: "I just don't get it. I'm so confused. Nobody's ever wanted to be nice to me before so why are you?" I've never forgotten her in all of my years of teaching.