My mother is depressed in a rehab facility and wants to go back to her assisted living apt. How do I help her do this?

Will she be discharged back to assisted living when she completes rehab? Encourage her with that information. "Yes, Mom, you'll be going back home to your apartment as soon as you are done with the physical therapy here." (If there is any possibility that she will need nursing home care instead, don't use this promise!)

Does her assisted living facility have physical therapy available? Is there any chance she could leave a little early and continue the therapy at the ALF?

I agree with jjariz that discharging too soon can create problems. Is Mom there for physical therapy, or is this a "transitional care" stay, where the main purpose is to regain strenght?

Talk to the facility's social worker that is assigned to your Mom. Find out what is their goal for her before discharge. Help Mom reach that goal. In my Dad's case, it was to was to walk 100 feet using his walker. Be careful of discharge too soon following surgery/hospitalization. They are sent to rehab in order to build strength. Returning home too soon sets them up for falling and returning to the hospital.