...when I loaded the game, it said that Pets was uninstalled, and that all pets would be deleted.
This happened to me once with OFB. It turned out that my .exe file had been deleted. Make sure that you still have Sims2EP4.exe installed in the following folder:
Program Files/EA Games/The Sims 2 Pets/TSBin
If it's missing, you can just copy it off the installation disc.