Raccoons usually don't stay in one place for long periods of time, so they may only be temporarily under your deck. If you can't enclose the deck to keep them out, try an animal repellent spray to keep them away (check out Havahart's line of products). Then, either close up the cat door, or install one that only opens for your cats, using a sensor or magnetic collar. Keep your garbage and food waste secure, and don't feed your cats outside.

You won't get rid of the raccoons completely - raccoons are territorial, and you live in this group's territory. But, you can keep them from bothering you. If they are still a problem, you can hire a removal service. What you can't do is kill them (at least, if you live in the city). You can't shoot them in the city, and if you poison them (also illegal), you run the risk of having a rotting raccoon carcass under or around your house.

You or them? Seriously: the raccoons are breaking into your house, holding you at gunpoint, and threatening your children? I live in a part of Seattle with a decent raccoon population, so "us or them" seems a bit dramatic.

It's not legal to kill or trap without a permit unless it's damaging crops or domestic animals, but the Fish and Wildlife site recommends checking with local authorities for specifics (link here). Eliminate food sources. The raccoons will go elsewhere.

God, don't arm them! The damn things are dangerous enough. I wouldn't necessarily bet on them not figuring out how to shoot you.

They're a real pain in the ass - they're generally completely unafraid of humans, they're very destructive, they carry zoonotic diseases and various pests that can infest your pets, they'll eat your cats, and they have the most noxious crap short of humans. But you generally may not kill them within city limits with impunity. I would suggest borrowing a Have-a-Heart from Animal Control and then figuring out how in the hell you're going to transport a trap carrying a really pissed-off, 35-pound, aggressive wild animal somewhere (and where you're going to take it), and how you're going to release it without it turning on you....or hire a removal service to deal with it.

Anyone who feeds baby raccoons - and yes, I agree, they're just as cute as hell, but they grow into big raccoons - should have raccoon shit piled on their bed.