I'll give you pointers, as i am the apparent cat person on DF.. But first....

as much as people cage rabbits and those rats with wings.. Caging a cat like that would only cause more problems..
And your welcome to drown anything you wish to within the laws of your city/state/country.. But personally, i don't see it as a viable option.. There ARE laws against drowning cats..

Now back to helping lilly....

It could be caused by several things... Male cats spray, but not till after puberty.. So at 12 weeks, it most likely isn't that..
Both sexes will pee on almost anything if the litterbox is 'full'. Full being that the wet litter in the box is less than 1inch below the surface. Or if the cats smell it too strongly..
note. If you can smell it, it's full to them!
If you change the type of litter you are using, they might not 'think of it' as the same litterbox...
If they try to cover up thier crap, and uncover wet litter, or more crap, they might look elsewhere..
Another common occurance with young cats is the simple fact that thier mother didn't have the time to 'teach' them that they should use the litterbox solely... It is about the same point as being weaned properly.. at 8 to 10 weeks.. Provided, of course, that the mother was trained to use a litterbox.. It's a common occurance with cats that are considered 'outdoor cats'.
And almost as common a reason is simpley that the cats feel they are being ignored..
But again, the most common reason is a 'full' litterbox..

Do you know which one is the culprit yet??