The mice can't do a thing until the shaman battle ends or truce is decided. The shaman would then build a bridge for the mice to jump on and enter to one of the holes.
The shamans may begin in a shaman battle or truce will be called. While in a battle, use drag balls on the other shaman to knock him over. Note that shamans spawn in front of their opponent's hole.
You may want to block the Pink hole after you win. Then, build a bridge to help the mice to your hole. Don't forget to use supports.
The pink's bridge is a bit more complicated. Start building a bridge, and when you can stand on it, you may want to block the blue's hole. Continue building a bridge, use supports. Before the bridge is done you will need to make a ramp to your hole.