Am I wrong for inviting her even though he will be there?

Sooo long story short , kind of long

I got married 3 months ago. It was family and a few close friends of mine. Everything was going good danced our ass off. As I was dancing with my husband I seen my BROTHER-IN-LAW dancing with another girl (my friend). My brother in law is married and his wife had just had a baby I would say 1 week. I didn’t expect nobody to come to my wedding from there part of course I understand she just had a baby she needs a lot of rest. Sooo back to the dancing he was dancing and only dancing but he also dance with someone else idk who it was a random chick so yeah. Before that my husband mention to me his brother was going to come for a little bit he said while he was at his brothers house he told his wife that gave birth “that he was going to dance at our wedding” his wife said “yes thats fine there’s nothing wrong with you dancing”

Him at the wedding:

*he never got drunken, nor he was drinking

*he asked his wife he was going to dance

*she agreed, that’s fine

*he never did nothing wrong

*only danced then he would go back to the table and sit down

*his a family’s guy, he wouldn’t do something bad like that

Ok anyway, as the wedding ended my friend the one my brother in law was dancing with came up to me and told me that one of my SISTER-IN-LAW ( a different person) had told her so many things like “why are you dancing with him” “ do you know his a married man” “do you know he just had a baby” “ his wife is at home”

I told my friend she should have never told you that

1. He asked YOU, you didn’t know he was married

2. You were minding your business sitting down at a table

3. His the one who came up to you, how are you supposed to guess who’s married who’s not?

I told her don’t listen to her she’s like that she likes to cause problems. So that happened. Also my friend respects peoples relationships.

It will soon be my sons birthday and I invited two of my closest friends and one of them is the girl my brother in law was dancing with am I wrong for inviting her ? He danced with another chick also and all they did was dance nothing else there was nothing wrong we all saw. I feel bad cause everyone will be there even his wife. Idk if he ever mentioned to his wife that he did end up dancing or not but I don’t want to look like the bad guy, you know? Should I invite my friend ? Or no