I understand completely about how you feel, but let me ask you this...How would you feel if it was your daughter and someone let alone family told you I'm having a party and your child CAN'T come because of something that was out of her control?
How did you explain it to him? and really think about it. Then think about how you would have felt being on the receiving end, then call him. Talk to him, don't lecture or grove, just tell him honestly how you feel about what your conculsions were. Than discuss alternative on how you can fix this, however be prepared for some very hard feeling.
I am sure it was not your neices fault about the lice, and she knows that her cousin that as you said feels like one of yours feels you don't want her there.
Now the lice issue....what I was told when we went through it was the cleaner the hair the better they liked it. Lice can grip it better, and once they are there, they well you know. What we found best to keep them out of the girls hair was, hair grease and we stopped washing their hair till the weekend. We hated their hair was so greasy, but it prevented any more of the problems. To get rid of it in the hair, put mayonase on their head and let it sit, or olive oil, it sufficates them.
Good luck hopefully your brother andyour neice will find a way to let go of the hurt they feel and you can stop feeling guilty.
Chelle