Go with the humane trap first and see if you have any luck. I find it's 50/50 on whether they work or not. Some mice are not interested and really can only be caught with a kill trap or poison.

I wouldn't recommend putting one in a cage. They are very cute, but diseases aside, they will try to escape at any chance. They want to be freeeee! o/~

I'm sorry you've had so many issues with the play so far. I'm guessing it's because the weather has been so crappy this winter. But I'm sure you were awesome!