You have two problems: the carpet, and the rats.
Carpet: call Wal-Mart, Home Depot and Lowe's. Explain your problem and ask if they rent carpet cleaners with the right kind of disinfectant. If they don't, they should know who does.
Rats: you need a rat-free attic. They are getting in somehow to nest (they can't live there full-time, because there's no food). Call exterminators and ask for a *free* estimate. When they walk your property they will probably spot the access points immediately.
Plug the entryways. Either hire the exterminator, or a contractor, or get your husband to do it asap. Then lay out poison in the attic to kill any rats trapped in there, before they chew their way out--sounds heartless, but rats carry a slew of diseases, and your children come first.
Buy $20 worth of rat poison. Get a brand with Brodifacoum, it is the best stuff. Put most of the trays in the attic, and a few under the sink and behind the fridge (child-proof these areas, of course). Then you can sleep easy. :)