@enchantress6274 If you can find the pet shop in the launcher, you can uninstall it from there, then reinstall it. If the launcher isn't working, you can use Method by Mell, towards the bottom of the article below, to examine the .ebc files (not .dbc, those are custom content) one at a time, which should make it easier to find and uninstall the item.
https://sims3.crinrict.com/en/2011/01/tutorial-how-to-get-rid-of-unwanted-custom-content.html
You may also have an issue with ccmerged.package, in DCBackup. This file is necessary to make premium store content work, and its corruption is one cause of the pet register disappearing. Since you're missing more content than that, this is unlikely to be your only issue; I'm mentioning it in case simply reinstalling the pet shop doesn't restore the register.
For ccmerged.package, the fix is to create a new one, which means installing all your premium content into a clean Sims 3 folder and copying over the file to your regular folder. Or you can borrow the copy that Nonamena has uploaded. Her copy supports all premium content, and it'll work whether you have all the content or just a few items. (It doesn't make items you don't own appear in-game, just the ones you've installed.) I can't link the site with the download here, since it's third-party content, but google should be able to find it for you.