Oh, hell no. You barely know the girl. The last thing you need is some dysfunctional family (all families are dysfunctional) at this point in your relationship.
Tell her you were invited to a friends and ask her if she wants to get together after dinner or tomorrow.
Thats what I did
To be fair, she was just being polite as I told her I had no relatives up here for the holidays
Tld my buddy last night afterwards I would come to their place for Thanksgiving