Whichever advice you are going to follow, do anything else before bringing it up openly, whether in a letter or plainly. Discussions like these can have long lasting ramifications.
Do you ever see active resistance to coming over, or do you just notice that they don’t initiate any get togethers. If the latter is the case, there is a lot you can do and initiate. But keep an eye out for their inner reaction. Never turn yourself into a pest or a tail.
So, it narrows down to, whether him or her, a disassociation with your family, without actively making you an exception. It can be him only, being that he doesn’t feel a connection. Although, you might ask, isn’t that the chicken before the egg? It may be, either him or her feeling a disconnect, being that you mothered her. A sister is never a mother, she is a big sister. The first step in getting ahead is to rise above or away from the biggers than you. It’s hard to know what it is, but for the last choice, you can search within yourself and ask yourself if it is possible that she would feel that way about you.