You will need to realise that she's undergoing a huge change in her environment, with her owner gone and new human, feline and canine roommates to get used to. It can take a dog up to three months to adjust fully to a new setting, so give her time and don't stress her out.
It may help to provide her with a crate that she can retreat to when she feels vulnerable or wants to be by herself. This crate must be associated with only good things (feed her in her crate, give her toys while she's in her crate, praise her when she's in her crate, never send her to the crate as punishment) and she must never be disturbed while she's in there (no yanking her out, no sticking hands in). Having a crate appeals to the 'den' instinct that a dog has, and it helps a lot in building security and confidence in a dog.
Handfeeding her meals is also a good way to build trust. Pet her, talk to her, take her for walks, but don't coddle her excessively, spoil her or obviously favour her over your other dog.
As for training, I would definitely go for positive reinforcement. I've always been a fan of positive reinforcement but in this case I think it is probably essential. You want all your interaction with her to invoke good feelings as far as possible, and training shouldn't be any different. Start with something basic like 'sit' and then start implementing NILIF (
http://k9deb.com/nilif.htm ) just to introduce some structure to her world.
In the meantime, I wouldn't leave her unsupervised with the cats. Baby-gates can help a lot in separating a dog from rooms in which the cats are allowed. If she is not openly aggressive towards them, I would let them interact briefly, but with her on a leash and with you supervising at all times.
