I think the pack issue is still in play...especially for a rescue dog. There could be a history of not having a pack or simply a matter of not knowing the correct dog language and behavior to establish a position. And not knowing where she stands at all can be stressful for a dog.
Make sure as you bond with her that you benevolently remind her that you are above her in the pack order. If you are sitting, she should be on the floor, not at your face level. Also, make an effort not to approach her from a position she might see as threatening. Ziggy over there<--flinches when anyone pats him on the head. We've had him since we picked him up from his mama at 10 weeks. He knows us well. We've never hit him or done anything to create this response, but still, it makes him nervous. So scratching his chest first, or under his chin, relaxes him, then we can give him a nice ear rub.
The pack order stuff really isn't as relevant as people think it is. Dogs know that we're not giant bald dogs. They don't need humans to do a clumsy pantomime of our interpretation of their body language in order to feel like they have a place in our homes. We lack tails, ears, scent glands, etc. which are all essential and subtle communication tools. They love us and put up with us despite all that.
Dogs are incredibly intuitive in regards to human gestures, and reading emotion based on facial expression alone. They are far better at reading us and taking cues from us than any other creature in the entire animal kingdom, including our closest primate relatives.
Approaching her in a non threatening way is good advice though. Small dogs especially can feel vulnerable, and we don't know her history.
That said, Nivarion, here is my advice to you:
1. Random treats alone are not enough at this point. I wouldn't focus on them too much.
2. NOBODY in the house is allowed to feed
or walk her, except for you. No treats or meals from them, at all. This is
very important.
3. Keep her meals in a ziplock bag in your pocket.
4. Tether her to you with a leash. If the exposure of a normal 6' leash is too intense for her right now, put her on a longer line until she's not reacting and under threshold. The idea is to keep her under threshold and not reacting.
If she's willing to eat out of your hand at this point, she has to eat out of your hands. Nowhere else. I'd also dole her meal out a few kibbles at a time throughout the day when she's being calm and non reactive. I'd also keep super amazing treats (like little slices of hotdog) on hand for moments of extra goodness when you need a little extra reinforcement or just as a random jackpot.
If she's too freaked out to eat out of your hand now, I'd toss her the kibbles while she's being calm and non reactive.
The idea is that every single good thing in her life comes from
only you right now. In reality, "alpha" dogs are not the biggest strongest fastest bosses who can whoop all the other dogs. They control the resources. That is all. In doing this, you control all her resources. You're also showing her that you're a friendly, non threatening person that gives her all the wonderful things she likes.
In regards to the peeing, that is a submissive thing. It's a puppy behavior and roughly means, "Don't kill/hurt me! I'm just a puppy!"
The fact that she's doing it tells me that she's anxious and scared vs. trying to disrupt the order in the house. When she does do it, the best thing to make it stop is ignore the pee completely and quietly clean it up when she's not looking. It's not a housebreaking issue, and since it comes from anxiety drawing attention to it will only make her more anxious and the behavior will continue. As she gets more confident around you she will stop doing it.