@Sarah_Ulmer I honestly don't know whether it's possible for people getting this kind of crashing to play with the Pets EP. So far, I haven't been able to come up with any suggestions that helped, and it's pretty clear in a lot of cases that the presence of one or more pets is the problem, in that removing them is an immediate fix. A few people have reported that they can't move in a household that already includes a pet but can adopt one later without issues. It seems to be hit or miss.
If you're willing to use mods and to experiment a bit, you could install NRaas Register, along with MasterController (for its useful commands), and ErrorTrap and Overwatch (for maintenance and error cleanup). Start a new save, use Register to set all the stray pet pools to zero, use Overwatch to shut down the neighborhood pet adoption scenario, and use MasterController to remove ("Total Annihilation") the existing animals in town. Unfortunately, the only way to stop inactives from adopting pets entirely is with StoryProgression, which is a heavy mod, both in terms of impact on performance and in terms of its effect on the game. But you could set it to the slowest pace and shut down most forms of progression for inactives to limit the extra resources it needs.
I don't know for sure that this will help, and it does take a little work to set up, so I'd understand if you don't want to try. But if you do, and you need more specific guidance, let me know.
It's also still possible that EA will identify the issue and patch it at some point, although I have no idea how likely that is. And of course if you get a different computer in the future, the pack will still be available to download from your Origin game library.