[notfarnow]

Now that you have a dehumidifier going, wash that mildew off with bleach & water.

Painting:
-Wash with water & bleach to kill mold
-Wash with TSP to really clean down to paint
-Prime with Zinsser BIN primer, you want the shellac based stuff, not water based

As for your little bunny, a baby gate is a good idea, as you suggested. We keep our bedroom closed off to our dogs in the day, but we like the heat from the wood stove downstairs to go in our room.

Our dogs see baby gates as an amusing challenge, and get through them within an hour or two. We're putting in a split bedroom door.