While wanting to be close to grandparents (ill or otherwise) is admirable, I don't know if it is the best topic for the "why transfer" essay. That might not be a nice thing to say, but I would wonder if an adcom would be inclined to think that A) you won't be fully invested in their college to get good grades, add to the campus vitality, etc, if you are drawn to take care of ill grandparents--it also calls into light if you can do that AND keep your grades up, etc and B) the transfer college would be made aware that they were chosen because of location--rather than their academic programs, a love of the campus mission, or a desire for a better education that you can not get at your current university. While being closer to your grandparents IS admirable, as an essay topic, it COULD be seen as a variation of "I want to go to your fine University because it is closer to my boyfriend's house."
On the other hand, I could imagine a well drafted "why transfer" that talked about your grandparents--but I imagine it would have to have mature themes in it, including ideas of sacrifice and some addressing of the issue of how one can balance difficult family circumstances with attending school fulltime... and not a bunch of hypotheticals, but perhaps some proven trackrecord of having already managed to balance these kinds of things as to allay any fears the adcoms might have of a student floundering because of having too much already on the plate.
Just my opinion.