I am happy to help!!! It's not often I can do these things, and what goes around, comes around, you know? I love Disney so much!
AKL is our home base, and we've stayed a bunch of times. The lodge is just beautiful- and I'd love to help you out, if possible.
As far as booking those rooms...gee, I have no idea. I asked the person on the phone how many rooms were available, and she couldn't tell me. So I guess it's first come, first serve, as far as booking it.
Let me call again tomorrow, I'm pretty sure I can book it now, and I'll get 30 days to cancel the reservation with no penalties. This way, at least I can go ahead and reserve the room, and this will buy you some time until you can get plans in order.
I don't know what rooms you've stayed in (we've stayed in both studios, 1-bdrms and concierge), but the studios are pretty nice, there is a king bed (I think...) and a pull-out couch. There's also a kitchenette, so you can make coffee, breakfast, etc. This saves money- we always bring bread, snacks, etc- and just buy milk and cold stuff when we get there.
How old is your daughter? There's all sorts of hotel activities throughout the day for kids- making bead necklaces, art, games, etc. So fun!
I hope this works out for you!