@buhcheeks Steam itself isn't supposed to "know" what packs you own in the EA App. It will only show content you've bought through Steam. The reason your packs work is because the EA App installed them and validates the fact that you own them.
This may just be an oversight or something that isn't worth fixing from EA's and Steam's perspectives. My First Pet Stuff is the only pack that contains content dependent on any other pack, and not many people would buy Cats & Dogs from EA and then specifically want MFPS from Steam. You could simply buy MFPS from EA and get around the problem entirely. It looks like the pack isn't on sale in Steam right now, and EA will have another sale sooner or later.
Having said that, I also don't see any indication that you need to own C&D in Steam in order to buy MFPS. The product page only says that C&D is required to access all content, not that its purchase is required overall. If that's not what you're seeing, please post a screenshot.