We bought a rabbit play pen (4 wire panels that link together) for our puppy to play in when we couldn't keep two eyes on him.

Another trick you can do is leash him and attach the lead to your hip, so you can feel what he is up to.

Now that Wookie is 6 months old, we've extended the pen panels across the wall with all of the wires on so he can't get at them and he has a bit more freedom in the living room.

I recommend Huggies Baby Wipes for getting rid of muddy paws. Also handy for a quick wipe down if puppy is stinky, but doesn't quite need a bath, also great for wiping up those few prints that get onto your floor.

A puppy is a big commitment, and your fiance needs to try a bit harder. I would have a nice family walk every evening. Try to get your Other Half involved more with the day to day training of your puppy.