It is very similar to coming out gay I think. Some parents are very upset at the prospect, but after awhile, many come to accept it. (Hell, look at Dick Cheney!)
So I would suggest that you keep not hiding your polyamorousness (is that even a word?). Treat it as if you were gay and they did not approve. If they want you over to their house and do not want your other partners, then you can respectfully decline. Eventually, she may meet your partners and realize everything is not as bad as she imagines.
I wish you well.