Thanks everyone, it's nice to get some confirmation of my suspicions. I'm happy to hear that meds tend to work well with rapid cycling, that gives me hope that the lithium will work (fingers crossed).

I'm hoping to try again without meds once things calm down a little (i.e. when the kids are sleeping through the night and life becomes a little less chaotic). In your experience, does rapid cycling tend to return once you go off meds?