potty training rescue pup

Question
A little over a month ago I adopted a 2-3 y/o cairn yorkie mix who apparently had be kept in a cage her whole life and not properly socialized to humans or dogs. She has a lot of fear issues which we are working on and she has bonded with me at this point but not my husband. I am doing all I know to do with trying to get her housetrained. I take her outside to the same spot each time very frequently (about every hour or so). I use a que word "go potty" when I see her begin to squat. I can't use treats like I would like (she is very food motovated) d/t she has an extremely sensitive stomach and I can only give her science diet for sensitive stomachs. But I do praise her alot after she urinates outside. I try SO HARD to keep my eye on her inside but she is so quick in jumping down and running behind furniture to do her job and it frightens her so much if I try to get her real quick when she does this. I have even tried leasing her to me but I can't get anything done because she will just sit down or pull back on the lease if it gets the least bit of tension on it. Therefore, I usually resort to toteing her in my arms alot inside unless I gate her in the tiled kitchen while I'm cooking etc (the rest of the house is carpeted).
How long does this usually take to housetrain a rescue?
Also, is the prospect of  overcoming  fears and being normal good in rescue dogs. I love her so much but sometimes I think I have bit off more than I can chew. But, then when I think of giving her back I just cannot do it. She has been thru soooo much trauma and I can't bear to see her go thru anymore. HELP! any suggestions are appreciated.

Answer
First of all, I liked your idea of tethering her to you.  If she sits, you can lure her up with a piece of food and say "stand", so eventually she gets the idea of standing on command:-)
As to the treat issue, if it were me, I would simply reserve part of her dinner to use as treats, and maybe hammer them into small pieces so you can give tiny treats, but lots of them.  It helps to use clicker training (if she's scared of the noise at first, you can wrap the clicker in a cloth, or use an "i-click".  The reason clicker training is unique and helpful, is that the dog is not being "corrected", which is even more frightening to a dog that is undersocialized. You can use clicker training to mark the behaviors you like - pee in the right spot, sit, lie down, and even click her for being brave and approaching a scary human or object.  More on clicker training: www.clickerlessons.com.  The more "vocabulary" you can teach her, the more confident she will be - dogs are less anxious when they know what we want!  Never scold for indoor accidents - that's when they learn "oops - it isn't safe to pee in front of humans".  So the tether really is your best bet, I just think you gave up too soon, and didn't consider using her dinner to lure her the first few steps on the leash.  If you're right there, she can't go hide it - you are right there to just say "uh uh - outside?" and then take her to the pee spot.