I would not advise spying. I can't see how that can help the situation.

From everything that you've said, it seems like your family is the hostile party in this situation and not your girlfriend. Have you brought home other girlfriends before? If this is the first one, maybe your family is jealous of her and afraid that she will take you from them. If you have brought other girlfriends home, how has your family reacted to them? Is this hostility a pattern with your family?

Some families do not like to accept that a member may be moving on and building a new family of their own. It seems like this might be the case with your mother and sister.