Small dogs are the hardest to get potty trained, because they are able to sneak off and go without being noticed, and catching them in the act is difficult.
Tricks I have used that work.
Feed at specific times, and let them out to potty right after, and keep them out until they go, this takes time and attention until they get a routine. Take the water up in the evening and make sure you do a good potty break before bed, that will stop the middle of the night stuff, just like with toddlers.
To keep them from sneaking off, I have a fairly short training leash, that I wear around my ankle, so the little stinker can not sneak off, you will notice the act much more quickly when it's happening by your foot, and then you can rush them outside to go, so the connection is made. Granted this can be a bit cumbersome, but it really does help them get it.
Dogs won't go where they have to spend their time, that's why they don't go in their crate. However if they can get away from it, they will go in the house. Reward for good behavior.
The other thing you can do, is hang a bell on the door that you let her out with, start by jingling it each time you let her out, show it to her, as she gets used to it, have her brush it with her muzzle. This is basically training them to ring a bell to go out. IT WORKS WONDERS!!! I had a dane, and a Golden that did this. My lab just wine at us, and then runs to the door to tell us.
The cat issue, the experts say that you should have a littler box for each cat you have, + 1. So if you have 2 cats you should have 3 boxes. I know extreme, but if you are having potty issues I would definitely get another box. Also try to limit access to those covered spots. If she is going in enclosed places definitely get her a box that has a lid, she may feel to exposed. Cats are hunters, and survivors, they feel vulnerable while pottying, that is why they like the enclosed space, they no one can get at them. Make sure you thoroughly clean the spots outside the box where she has gone with an enzimatic cleaner, like natures miracle, to completley get rid of the smell, otherwise she will continue to use the same place over and over.
Hope these answers help.