My Mom was just placed in a rehab/nursing home. Can I just get her released, and bring her back to live with me?

You would be doing so against medial advice (AMA). AMA signouts can leave you with huge medical bills. The MD would have to clear her for air travel, and I doubt that would happen. Airline travel exacerbates dementia, the changing air pressure in the cabin can leave permanent damage. I have been in rehab for a knee replacement, the meals were good, the staff was nice and my roommate was a constant companion. I got PT seven days a week and that helped my progress. Pain management was excellent. I could roll right into the shower on my wheelchair, grab the rails and sit while I showered. Forget your guilt. I felt like I was on vacation, and quite pampered.

It is usually a mistake to remove someone from rehab before the goals have been achieved. If living with you in WA is a good idea, it can wait until she is done with rehab.