Is it cordially invite or invites you?

It depend on how the user intend to use the sentence and so both are correct in the sense that when using it for a single person, it will be ' the family invite " and when using it for two or more or...

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.

cordially invites

If they are very good friends of yours then either phone the wife or husband that are getting divorced and see how they feel. If one won't come because the other is then you will have to tell them...

Well if you know her pretty well and she thinks you like her and you think she likes you than maybe you could tell her you only wanted her over but i don't know exactly what you should do this is...