JM had a fix for this in the ofb testing directory (
http://www.moreawesomethanyou.com/ffs/ofb/test/) called 'tombstonemovefix'. I don't know if it's Pets-compatible (or even still needed) since I haven't moved any gravestones since installing pets. But it's worth a try.
I wanted to send an update, just today, had my first Elder pass away (after getting feedback on my previous problem). Sent the tombstone to my community cemetary and there was no double death hit for my kids/toddlers. Thank you for leading me to that hack.
On a related note, i have found that those lots work better for my visiting sims, if they are owned by a sim, who then goes and closes down that business (using BRY). That way there aren't 8 or 9 useless sims wandering about, causing havoc and destruction while my sim is waiting to see a ghost/chasing a ghost so he can be scared. lol I haven't tried using a non-owner as a visitor, to see if other sims show up or not.