First, I would love to hire you to come over and clean my house:) I am not a clean freak, but have been lucky not to ever have had mice in my home. However, at our shore house, the mice are a problem. The house is right on the sand, and we have found they come in under the kitchen sink.
You do need to find where they are coming in. It's probably a really small spot. Look for some wood shaving that they have chewed through. We plug up the hole with steel wool, then my dad usually goes back and uses some type of expandable spray insulation. We haven't had any for about a year, so feel pretty lucky. Our house is unoccupied in the winter, which is when the mice move in.
Come spring, we have to get them out immediately.
Typically, I would bring down my 5 lb very ladylike and snobby cat. She was a great killer of all small things. One year my sister brought her two big and fat cats. They did nothing for 2 days but lay around and watch the mice.
I brought Princess, and she dispatched 8 mice in less than 20 minutes. The following day, 6 more. She definately was the hit of the household for her work! Maybe you can borrow a friends cat who is a known killer?
I would make a bleach and water solution, put it in a spray bottle, wear gloves, and old clothes. Spray down ever surface (and be sure to wear some type of eye covering). This should kill any germs the mice might leave behind. I would also very carefully inspect all your dry food items to see if you find nibbles at the packages. Our mice chew through cereal, dry milk, crackers, etc. Through away anything you might be suspicious of.
Good luck...oh, and the shelters are full of cats now. Burlington County Animal shelter has reduced their adoption fee to around $20 for a nuetered cat. You could save a life, get some love, and keep your house free of critters.

Probably not necessary, but you could have the carpets professionally cleaned if that would make you feel better.

I had mice this winter. It's a small house and there are not a lot of places where food is kept. I made absolutely sure there were not even crumbs anywhere (nor dishes left in the sink, or food left on the counter) and also made the garbage inaccessible.
I got rid of the mice over two weeks by using snap-traps baited with peanut butter.

You might want to make sure that, for the next while, your kids eat food ONLY In the kitchen and dining room so that you can restrict the areas where the mice might be finding edible stuff. You'd be amazed how easily bits of popcorn or chips end up under sofa cushions.
Check also in places like where the lunch boxes are kept, or the dog food or anything even remotely edible. A friend found that some pre-school ornaments made by her daughters with painted macaroni were chewed right down to the cardboard.
Consider also sources of water. I found mouse droppings INSIDE the portable dehumidifier. Imagine that packet of fun to clean up!

Mice get into the tiniest spaces. In the end, no one will clean that up as diligently as you will.

Like you i am also a clean freak. I also have a child aged 2 and knowing how messy kids can be i hoover at least once a day, pots are never left, clothes are washed straight of the back kitchen floor is swept and mopped maybe every other day (although i dont move my fridge, lol) Anyway my story is i was lay in bed about a fortnight ago and i was just lay watching telly and i heard this pitta patter on the floor and just assumed it was the dog. I shouted the dog and he was still downstairs in his bed. So i turned of the telly and listened and after a couple of minutes there t was again. So i shouted my husband who was watching tv downstairs and he came up and lifted the bed and there it was i lil tiny mouse under the bed. Well iscreamed and then he screamed (puff) and we shut the door and slept downstairs. Three night we kept it up until on the fourth night we went upstairs with the garden spade in flipped the bed to get the lil sucker but there was nothing there apart from dropping, so we decided to stay at my mum's house until we had the situation under control. Two weeks on we havent caught anything we have found the way there coming in by smudge marks in a storage cupboard at the top of my stairs. So we blocked of this hole and set traps in there and have a couple in every room in the house. We called our local council and they came and said we had took the right precautions by getting rid of clutter in cupboards and laying traps and there was nothing more he could do. So to this date we have only caught one in the bedroom and 2 babies in the cupboard. We are still staying with my mum until we are 100% certain they have gone. We are currently saving to move home because i know i will constantly be listening and watching for them. So you are definately not alone. From one clean freak to another lol.

You moved out of your home because of a mouse?? You are saving to move because of this? Good lord, people have been living with mice (and worse) for thousands of years. There are probably more fleas and germs on your dog than on your mouse.
Yes, they can carry disease, but so can your dog, or your husband, for that matter. They won't chew on your toes while you sleep, either.

Set your traps, remove ALL sources of food, try to find out if there is a way to seal the house up (this is rarely possible) and get on with your life.

Certainly, closing a door to lock in a mouse isn't going to work - these things'll fit through a keyhole :)

I'm with you, Chris! Declare war!!!! and set all kinds of traps. Of course, you'll have to have someone willing to dispose of the traps (I don't empty them, I toss the whole nasty mess using a pair of pliers to carry it. I know, a source of hilarity for several, but that's my story!) I'm currently doing battle with them at my mom's. She's not able - old farm house - and not much help from siblings so far. So my weekend only attacks are limited...but attacks they are! To be fair, my bro emptied two traps for me; I scalded them, & re-baited. I've fought mice in more than one house, but never did I consider moving out....I figured *I* was paying the rent/house payment and THEY were the uninvited, unwanted poachers of my turf!