I dont get it...

This is worded a bit strangely but I assume you mean that you got a new supervisor at work and your girlfriend told you he’s her dad. Shouldn’t be an issue if you do your job right and you treat your girlfriend well!

In some cultures (this doesn't say where you're posting from) you have in-laws from the time you're seriously dating someone. That's the case where my wife is from, and it certainly made our dating a bit odd, since you were essentially "dating" the family as a whole. Fortunately my in-laws a super chill and good people!

Is the FML that you work with her father? Or is the FML she has already planned your wedding?

I'm not sure if your girlfriend's dad is your supervisor or if you are cheating on your wife with a girlfriend who found out that your wife's dad is now your supervisor...