I fixed the problem. It was a corrupted data file.
You go to "my documents" then the rom folder then go into the affected characters folder and delete savevariables.lua.
Yep. This problem has been around for ages, and the solution was always this. There is very little in that file that is of any consequence, unlike the main savevariables.lua, and deleting it tells ROM to make a new one, which doesn't cause the problem with pet menu.
As a reminder.... guys, back up all of your savevariables.lua when they are clean. Much easier to restore than recreate all your settings.