I've noticed that even though my dog whines that it has to pee after being potty trained, if I leave her alone she will eventually go outside to go. Have you waited it out, or are they going in the house if you don't let them out?
Also as far as the constantly scared thing - do you mean from their fears, like the oven being on? Or their portrait is always red and they're yowling because they're scared, and if you ask what's wrong your pop up says they 'just need a moment'? THIS is a known bug that comes from getting them a check up and the preventative treatment at the vet. You can fix it by using the remove buffs cheat, with their sim ID