Candor - OMG - that situation would drive me crazy. Your patio has to be for your use only with that definition of "limited common element." I bet the spigot is just for maintenance use.
Is any other part of your unit like a front porch or walkway a limited common element? If so, maybe you could ask for clarification from some of the other board members about what this means in reference to one of these other areas. Or just ask about what the term means in general. (I'm thinking it might be best to get an answer before board members realize where you're going with the issue.)
I'd be tempted to buy a watering can for the neighbor and give it to her, telling her to fill it in her kitchen and stop using the spigot on your patio.