Re: cat scratching
Desdemona really liked to scratch on our rug. One thing that helped us was to cover that area with "acceptable" scratching surfaces - sisal mats, a scroll-shaped scratcher, cardboard pads. And when she used the acceptable surfaces, she got praise, scritches, and/or a treat - positive reinforcement for the desired behavior. Eventually we were able to move those scratchers off the rug, and she has pretty much left that rug alone since then. She uses the cat tree (carpet-covered, she loves it) and scratching post too, but she still really likes horizontal scratching pads on the floor. So if it's just one spot on the carpet that they're really going at, maybe try putting cardboard or sisal scratch pads over that spot, and give them good positive reinforcement when they use those. Or you could try adding a carpet-covered scratching post, if it's the carpet texture that they like. Hope that helps!