If she’s been living in a cage at the pound for a while, she may be confused.
I’ve housebroken all three dogs with this method, and I think it’s the best of all the methods I’ve heard: For the first couple of weeks, take her out every two hours during the day-- if she were a puppy, I’d say every hour. (At night and while you’re at work, crate her.) I know it’s a pain in the butt, but the best way to fix accidents is to prevent them from happening at all.
Praise her lavishly every time she eliminates outside. I suggest that you coax the dog verbally while you’re waiting with a phrase like “hurry up” so that when you’re travelling, she’ll know that even though this grass is not in her yard, it’s okay to pee here.
Gradually increase the time between outs to a schedule which seems to suit both of you. My dogs go out in the evenings at five, nine and once more before bed at eleven. Let the dog out if she whines, but once she gets used to the schedule, she won’t cry to go out at other times unless her tummy’s upset.
Take her outside every time she whines, even if you know she’s wanting something else-- this will teach her that the “signal” for going outside is to whine. (Do it immediately, or else it won’t click.)
Are your stairs the same color as the floor below? With some dogs, it’s almost like an optical illusion-- they can’t see the stairs if the color blends into the floor below. At my old house, I tacked tread pads to the stairs and after that, the dog had no trouble.
I had a lot of trouble when I got my second dog. My first dog was very hostile to the newcomer, and it was months before she would accept the puppy being within five feet of her.
Make sure your first dog feels that her status has not changed. Show her as much (if not more) affection as you did before the new dog came. When giving out treats, give it to your first dog before you give it to the new one. Reward the first dog whenever she has a positive interraction with the new dog. Give your first dog a private area where the new dog is not allowed, so she can retreat to her “territory” if she wants to. Don’t make your first dog share a food bowl with the new dog.
Otherwise, let them sort it out. Likely, there will be tussles as they sort out who will be dominant. Don’t be alarmed at growling scuffles-- unless someone squalls in pain or actually gets injured. It’s unlikely that it will go that far, though. The scuffles may sound and look violent, but they most likely won’t hurt each other. However, just to be sure, introduce them cautiously to one another’s company. Keep both on a leash, for example, so you can tug them apart if your first dog looks like she’s going to attack the other dog. (Look for raised hair and slicked-back ears. That usually means a dog is going to get violent. If the dog’s mouth is hanging open, with the ears perked, it likely means they want to play and their fighting is just wrestling.)
Get Ginger a crate. You’ll need it for housebreaking, and likely, she’ll start thinking of it as a safe place. My dog likes to nap in his crate, and he retreats there if the older dog has growled at him. When you travel, you can take it with you, and Ginger will feel better because she’ll have a little piece of home with her.
If Ginger wasn’t properly socialized, you may always have issues. You didn’t say much about her temperment: is she shy around strangers? Is she submissive or dominant?