Everyone is different but with only knee coming home should not be a big issue. My basic belief is that there is no place like home. I can control when I get up, sleep and keep my meds on schedule without waiting for someone to dispense them. I can ice as much as I need and again, do not have to have someone remember to keep me iced and elevated. Again, part of the reason I had one knee done at a time is that I knew I could come home with one knee only operated easier than with two. My other reason was work - so I could space out the time I was away even though I did do both knees in one year.
If you do go to rehab, investigate it throughly ahead of time to make sure they deal with joint replacements and are organized around what is needed post op -- ice,elevation and pain meds on schedule. Some rehab facilities are not tuned in to the recovery and some of the forum members have had issues from lack of support in those directions.
Best of luck to you and just focus on the fact that soon you will not have that awful knee pain. Lee