I've had pet mice before, and yes, they can get ANYWHERE... basically anything they can poke their tiny noses through, they can fit their bodies through. When I had mouse cages with bars, they constantly got out. I finally got out of those plastic habitats which eventually put a stop to their escapades (although you gotta make sure they're closed properly!!).

I strongly suggest that you either get rice sold in a resealable bag, and/or get a large airtight container to store your rice in. Remember that there are other things besides mice that can also get into your rice, like lice, weevils etc. Mmm... unwanted protein...

If you've found droppings and you can hear them, then it definitely means you have mice. Get some mouse traps -- I find baiting them with peanut butter on bread works really well. If you and your wife are too squeamish to look at or handle dead mice (note: sometimes the trap doesn't kill them, sometimes they escape or it just breaks their neck but they're still alive) you can get special traps where the bait is on the inside and when the mouse goes in, the trap shuts and in doing so literally breaks the mouse instantly. The trap cannot be reopened, so you just chuck it away (you can't see the mouse as it's shut inside).

For more humane measures, you can also get mouse traps which only trap the mouse but don't kill them - usually hardware stores will have this (I used to use them when I wanted to trap my escaped pet mice!) But erm... make sure you don't look into the trap from below to see if it's worked and trapped a mouse, cos when the mouse is trapped it freaks out and unloads its bladder and bowel contents (and you don't want that falling on your face!).