Please do try to see that this is quite natural, especially if this is the first time your granddaughter can remember a visit from her other grandmother.
As others have said, there is a good chance of your and your granddaughter's relationship getting back to something like its old footing as long as you manage to conceal your hurt.
On the other hand, a girl of 12 is reaching the stage where she will naturally start to move away from family and other adults who have known her and whom she has known all her life, so you would be wise to accept that things are going to change.
Being widowed does make one emotionally fragile, especially if you only recently have lost your husband.
Try to make new friends and take up some new interests to lessen your loneliness - you neither can, nor should, expect your daughters and granddaughters to supply all your emotional needs.
I apologise if this comes over as unsympathetic - it is most assuredly not meant to, as I do understand why you are hurt, but I would hate to think you are storing up more hurt for yourself by taking a natural development of new interests in a 12 year old girl too much to heart.