That is one sad looking pound puppy! I have a Radeon HD series graphics card and It looks like the same problem that drove me insane. It started with the horses. They had transparent areas, like your pound puppy. With movement, like jumps or horseplay, the main and tail colors shot linear across the screen. There may have been a game update, but I don't recall any other change. I re-installed the game, expansions, store, and left out the cc and I got lucky. My son's friend fixed it in maybe 20 minutes.
Go to the AMD web site and download the latest recommended drivers and software, which I think the Radeon HD series uses CCC software and best guess, what caused the problem. Make sure the CCC software is at (Windows?) Default, unless you know what you are doing. As explained to me, the graphics card software settings will be used over those set by the game (Sims) and can cause the game to display incorrectly, just horses and dogs with Radeon HD?