Yes she had survived heart surgery and a stroke, so a temporary stay for recovery might have been understandable whenever that was, but as we know her in the show it was in her past and at the current point of the show, she had every bit the energy and activity of anyone else in the show. It has always struck me as odd.
shareI agree, in reality, a stay in a home for rehab would make more sense.
But, in the reality of the show, we have to suspend disbelief. Sophia's stoke supposedly left her with "no filter," blurting out anything that came to her mind. That's where most of her humor came from.
It's easy to assume that her cantankerousness could be taken for a mental deficit or aberration -- leading to the assumption that she needed care. Perhaps Dorothy felt she couldn't handle her (we're not shown that part).
Her degree of "energy and activity" would have little to do with her cognitive powers.
Again, suspend disbelief. Things in sitcoms seldom follow the norms of real life.