Forget about trying to "train" obedience into her. If she was a dog that was receptive to this, it would have happened already, & the likelihood of your accomplishing it to be adequate for keeping her safe without putting other precautions into place is low. That doesn't mean she wouldn't benefit from some form of training, so by all means, meet with the trainer & find out what you can do to make the transition smoother, especially in helping her to adapt.
Regarding keeping her safe, these dogs are notorious for having a mind of their own, & an impulsiveness to darting. Since there is a fenced run in the back for her, I am assuming you can leash-walk her to it & it will be secure for her to stay in? If not, & the backyard is a problem, consider getting a temporary fence. We have the green garden fence (comes on a roll, & is put up on metal stakes that are stuck in the ground.) There are a variety of heights & colors, it is easily pulled up, and because you stake the ground before hooking the fence, you can make it any configuration that you need.
Regarding doorways in your house, you can get some type of gating for inside the house. What would probably be most ideal is a dog exercise pen that you can arrange in a semi circle around the doorway, with either a short height that you can walk over, or a higher pen with a gate that you open, once the door is securely closed.
Garden Fencing: http://www.acehardware.com/product/index.jsp?productId=83...
Exercise Pen: http://www.amazon.com/MidWest-Exercise-Pen-30-Inch-Black/...
These are just examples - the ex pen you might even be able to find on Craigslist in your area, but can also be gotten at most pet stores, & even some places like Walmart or Fleet Farm/Tractor Supply.
Hope this helps! T. :)