Is it a government job? If no, then there is no reasonable expectation to privacy and there is no first amendment protection.
It's simple and most grown ass adults don't understand it: Don't write/post incriminating shit on Facebook. Most people don't comprehend that posting something on Facebook is like posting something on a giant bulletin board you would see in the hallways on a college campus. You post it, it's out there.
If this a hill you are willing to die on, OP? If so, do what you gotta do.
Check your contract, check your employees' contract, go through them with a fine tooth comb, and if there's nothing about social networking then the VP doesn't have a leg to stand on. Keep a record of everything he says/does with regards to this particular situation though, in case he finds another reason to get you out, then you can show that the real reason was an illegitimate one and bang his buns bright blue in court.
Yeah.... no, she would lose in court.
There is probably nothing in regards to Facebook in their contract, however there most likely is something in there about harassment/disparaging a co-worker etc etc. Making disparaging remarks about the VP (IE calling him creepy etc etc etc) falls under that and that is what will get her in trouble.
Potentially getting fired for harassing the VP is not exactly wrongful termination.