dotty342kids I wonder if your mother is over-anxious and abnormally sensitive about not intruding on your family life. Grandparents, especially perhaps grandmothers, are often very conscious of the fact that they are not the parents and are concerned that their sons, daughters, sons-in-law and daughters-in law might see their well-meant offers of help as interference or trying to undermine them. Consequently, they can come over as uninterested, even uncaring about their grandchildren. (Being a granny is lovely, but it's not all plain sailing.)
When she visits, perhaps it would be helpful to get her involved with ordinary activities with the children, such as bath-time – with you to begin with and then, maybe, on her own. Why not ask her if she'd like to read the bedtime story? You haven't really got anything to lose. If she's says no, nothing has changed. If she says yes, then it might be the beginning of a closer relationship for all three generations.
By the way, although you and your father are estranged, you shouldn't underestimate how his illness affects your mother. You mention that you have no uncles and aunts or siblings, so your mother may also lack loving companions to confide in about her concerns and worries, including your father's health and the prospect of widowhood. I wonder if her mentioning about staying where she is now and moving nearer to you when she needs help might be her way of trying to establish a closeness without suggesting any kind of her taking over – albeit confusingly put and pretty inarticulate. It does sound to me that communication between the two of you is perhaps not as open as it might be. Maybe the way forward is for you to try to be a bit more open yourself and see how she responds. This does not mean that I am suggesting that you are in some way at fault, merely that the remedy for a situation that is clearly making you unhappy and, reading between the lines, your mother unhappy too, lies in your hands.