It sounds like she's using the sippy cup as a "soother" maybe? I'm not suggesting that you introduce a pacifier b/c I think that may be more harm than "good" at this point, but you might want to consider having her transfer the soothing to a stuffed lovey or another "non-dripping" item.
You are going to want to fight this battle sooner than later- it's really no different than having a child wake-up to nurse or drink milk throughout the night at this age. She needs her sleep and so do the rest of you! She's also getting close to potty-training time and most "experts" suggest eliminating fluids for an hour before bedtime during that stage.
Make sure that there isn't anything "medical" going on (not getting enough fluids during the day) and then have brother sleep in your room for a few nights and... yes, I'll say it... CIO.