Can I take my mother out of rehab after her stroke?

Yes you can. It will be called discharge Against Medical Advice (AMA).
I would first check with her PCP if she/he can order therapy in the home. If he is willing and someone will be with Mom 24/7. Homecare will evaluate and tell you what Mom will need.

Be aware that Medicare only pays for 20 days 100%. After that its 50%, hopefully her supplimental will pay the balance. If not, she will be out of pocket for the rest. About 150/160 a day. My Mom was in rehab to get strength back. I told them they better do what they needed to because she was not going to be in any longer than the 20 days. I was pinching every penny to keep her in an AL.

Not sure how they can determine the time she will be there. Medicare determines that by her progress. Don't let them tell u insurance will not pay. Its a scare tactic. They will. If u find the PCP will give orders for home therapy tell the Director of nursing you want Mom discharged. That you have made arrangements for Homecare. Your Mom is not in jail. She has rights. If they refuse, call your State Ombudsman.

For the future, you do not have to go to rehab. I wish I had thought of homecare when my Mom went there. It could be done at her AL.

I disagree with others. Your mother, if competent, can sign out AMA or against medical advice if she is competent to do so. If someone is appointed as her Medical POA, then THAT person can assist your Mom, if she is incompetent, in signing out AMA. However, if there is a doctor who says that your mother needs PT and OT, I would attend a care conference with a Social Worker at the facility and discuss with all entities from dietary to OT and PT to see what is being accomplished for Mom and how she is doing. No one likes this. My bro called it his "incarceration" and still refers to it in that way. I will tell you they had him walking so well, his balance so improved, and had him in so much better shape after about 28 days that I couldn't believe it.

What kind of therapies are they providing for her?

She should be so worn out from all of the physical and occupational therapy that she should not have time to get depressed.

I would visit more frequently, encourage her to participate in activities available at the facility and make sure that she is getting intense rehabilitation.

If that isn't happening, she may recover better with in home health.

No entity in America can force a competent adult to receive medical care or rehabilitation. No matter what they tell you.