Pests nesting in the coop

I'll give a backstory of my setup to help clarify first.

I have a 2 story, outdoor brooder that used to be a chicken coop. The top part had a ramp that led to the bottom part and the bottom part has a door that leads to the run. The run is closed off and the top par of the brooder is blocked off from the bottom part. The chicks are being housed in the top part of the brooder, that is accessible through a top hatch that has a plexiglass viewing window, that latches. It is heated, and insulated and has deep shavings for bedding. It stays very toasty warm for the chicks in there and I haven't ha any problems until tonight.

I went out to check on the babies and lo and behold, there were mice eating right out of the feeder! I opened it up and they burrowed deep into the bedding. I tried to dig them out but couldn't find them. I went inside for a minute and came out and saw the bedding moving again. I grabbed what I thought was a mouse, but it was a baby MOLE. A mole! Needless to say, my dog ended up killing it.

I for sure saw at least one mouse, the other two could've been part of the mole family. I have no idea how to handle this.
The chicks are between 1-3 weeks old and I really don't want them getting sick from the mice or the mice chewing on any of the wiring. Plus moles are really not our favorite creature, they destroy our yard. Help?

 

I would've taken a picture of it, but in pretty sure my dog has pretty much eaten it...yuck. But yes, it was a mole. The feet were very fat and paddle like and it almost looked like it had no eyes. It was very small, probably only an inch and a half long. The mouse was pretty big compared to it.
I don't have any traps, but I can pick some up today. I figure there's probably more that I'm not seeing. The shoebox idea is great and I'll try that tonight and see what happens. Thanks!