Thanks for taking on this rescue girl. As you are discovering, puppy farm dogs can have far greater issues than a lot of other rescue dogs -- not always, but many take a long time, and some never fully, recover from this experience. Most dogs do gradually recover but they need a LOT of time and patience. It's great that you have the other two dogs because most rescues of this type find it much easier to learn to relate to other dogs first and she will learn from the other two that you are OK to approach.
Please have a read through the links I have on rescue dogs and advice on owning or fostering, at the top of this rescue forum. These should greatly help.
In general -- from the sound of it, you are probably pushinbg her faster than she is ready for and expecting more normal dog behaviour than she is capable of at this time. Housetraining may be be a big challenge. And not all puppy mill dogs ever totally get housetraining. Just be kind, consistent, try to never let there be an accident by always getting her outside so that she is set up for success and rewards, never, ever failure.
You need to train her as if she is a puppy, with no knowledge at all of going outside. As she has spent her life going in a cage she has little to no concept of keeping a den clean and this can make housetraining very hard -- just be prepared that this may be tough for you to address. Or she may just start to 'get it' and do fine.
Try her on a soft harness -- this is much more comfortable than trying to walk a mill dog (or any cavalier) on a collar and lead. Walking may also take a long time. There's advice in the links I think on how to get a rescue dog comfortable with a harness and lead (eg let her come and sniff them and leave them around the area she plays in so that they are not alein to her and smell 'normal' to her after a while. Let her wear just the harness while inside and without the lead being attached. After a week or so of gradually increasing the time she has it on, then try the lead for a few minutes and gradually work up). She likely doesn't really need walking, so try playing with her or just letting her play with the other dogs in the garden for the time being as you get her used to the harness and lead; and don;t try to rush her into something totally alien to her such as walks, until she trusts you and the harness/lead a bit more.
Check that your body language isn't scaring her. Approaching a dog and leaning over her, reaching towards her, looking directly at her are all things that dogs read as potential challenges or threats, especially for an undersocialised dog. Hands reaching toward her in her past probably meant manhandling or being hit, being thrown into different cages or into a room to be mated, never kindness. To get her used to you, use treats to reward her for coming to you, squat or kneel down, don't look directly at her, hold out treats quietly, let her come sniff at you and take the treats; don't try to reach for her or pet her, just quietly praise.
I recommend getting the manual on working with shy dogs from
www.deesdogs.com too.