Hi Bogie!
I can't say for sure if this will work for you, but maybe it's worth a try. At one time, I had a duplicate folder for screenshots on my desktop. The game would save them in both locations. So, try going into Explore, click on Documents, Electronic Arts, Sims 3. Then right click on the Screenshots folder and select Create Shortcut. The new shortcut folder will be in the same location as the Screenshots folder. Then right click the new shortcut and select Send To and you'll get several options for various drives on your computer. I think that maybe if you select the location of your new X drive, you'll be able to get your game screenshots there. I don't know about completely changing the target location within the game, but this might be a work-around for you. Please let me know if it works.
And yes, I can sympathize about the cats! I have four of the darlings and they sometimes get a little rowdy! =^..^=