I need a cat whisperer

I need a cat whisperer.  My cat obviously has a 'tude.  Can't you just see it in this picture? Someone needs to whisper to her and tell her to stop peeing on my throw rugs and carpet, 'cause yelling isn't working.

This cat was my kids' first pet.  She arrived on our deck six years ago with her mama and sibling, all feral. We weren't able to handle the sibling and mom, but she came right up to us.  My daughter begged to keep her, and I quickly told her she needed to ask her dad when he came home.  Let him do the dirty work, I figured.  However, I did not expect a few seconds of eyelash batting to be so powerful, and we soon owned our first pet as a family.

All started out fine, until we began introducing more animals about five years ago, one more cat and two dogs.

Offender #1

Offender #2

Offender #3

Even then, things were not so bad.  She just kept to herself, occasionally gave a swat or hiss, and spent the rest of the time giving dirty looks.  Then, about a year ago, she started leaving little deposits "in order to keep the dogs away", according to the vet.  The dogs just thought she was leaving them treats (ew).  However, the last several months, she's been a bit more outspoken. All over my carpets. I haven't caught her in the act yet, but I know she's the guilty one. Each night she has been perching herself outside the laundry room, which contains her box and food, and guards her territory before the dogs go to bed, eyeballing them if they get too near. This cat is evil has issues.

I'm really desperate here.  The vet says this is purely behavioral. We've added new boxes where the dogs don't roam as often, to give her some more space.  It has only created new territories for her to claim and christen. I've tried containment at night in the laundry room, which makes her more angry. A few people have told me to cage her for 6 weeks to retrain her.  Does anyone have experience with this in a territorial situation?  She knows where she is supposed to go, she's just mad at the world.

She can't go outside as she has no front claws and isn't very "street smart", based on the couple times she's slipped out and returned 24 hours later starving. 

I'm afraid we are going to have to get rid of her.  However, I'll have two devastated kids. Suggestions?