Is it The Family invite or The Family invites?

The correct grammer would be "the family invites you". "Family" is singular in American English, and therefore should use the singular form of the verb.

Offer to pay for it but tell her the money is contingent on your guest list.

Etiquette states that the bride and groom's families can invite the same amount of guests. However, depending on the finances of both parents (especially the bride's parents) it's wise for both sets...

I was in the exact same situation! I really caused a scene... Here is some of my hind sight to help you out! Deal it with it with the biggest smile you can manufactor... That would aggrevate them...

It would be best to say something like: "The group will be meeting at ____ restaurant. Everyone should plan to pay for his/her own meal."