The sharingan is open to either men or women if they develop strong bonds with someone else.
The problem with female ninja isn't that they're weak, it's that they never really become attached to anyone so they never develop bonds that can be severed, which prevents them from actually developing a sharingan.
Uchiha women are like any other female ninja.
Cold distant witches.
Uchiha mothers don't love their sons, as evidence by the fact that they let their children murder each other, and they probably only stay with their husbands for the money (they're still good ninja, which mean they have a little money).
So in short, the sharingan could very well be activated by a girl, but she'd need to develop actual bonds with another human being, and i don't see it happening.