I would do the one at a time.
When you say "rehab place" do you mean a physical therapist or a nursing home?
I once stayed in a nursing home for a couple weeks. Actually it was twice, and I didn't like it. I'll never rehab on one of those joints again. I will go home for my rehab. The food is bad and they never get your meds right.
My first nursing home was a Catholic one on the corner of Murray and Farmington. The second one was a VA one in Vancouver adjoining the Vancouver VA hospital. The VA nursing home, like the Portland VA hospital has food that you can't keep down. My first hospital stay that included a stay in the ICU for about three weeks served food so bad that I literally threw up every time I tried to eat it. I lost 40 lbs. My wife started bringing in food from a restaurant or, better yet, from home.
My advice? No nursing home.