S.M.
1st i would make sure the things were true, if they are and it is a big enough deal that you dont want her around yoru family for a birthday part i would be honest and tell her, " i understand you ____, and im really not comfortable with that so i would appreciate it if you did not attend this event"- it will probally come off as a little harsh- but im assuming if you dont want her around you and yoru fmaily for a bday party, you are not trying to be her friend either...
i guess i would make sure it is something that you really dont like because any way you say- you will have to be upfront:) gook luck