Hard to tell from this what the issues are exactly. Does your mother have mental health issues? Is she an alcoholic? Is her lack of interest something that happened suddenly, and if so, do you know the cause of it? Or is it a longstanding lack of maternal interest going back to your childhood that you hoped would change with grandchildren?
My own parents have been quite distant for long periods. They divorced when I was 17 and seemed, for some years, to lose all interest in me. I was such a mess by the time they divorced that it was like they created a huge mess and then just split, with each blaming the other for the disastrous outcome. So I have some familiarity with the pain of parental rejection. In my case, once I had worked on my feelings of abandonment in therapy and 12 step recovery (for children of alcoholics and my own alcoholism), that reconnecting with both of them with as much cordiality as I could spare without causing myself undue pain has been helpful in establishing my sense of myself as an adult whose standards of behavior are those I choose, not simply a automatic reaction to the behavior of others. I've found that if any action I take is tied to a hope that I would finally get the love and approval I've yearned for since childhood, it sets me up for pain, but simple, low-key acts of friendliness such as occasional brief emails, birthday cards etc., don't cost me much and free me of the lingering guilty feeling that I am somehow in the wrong, somehow causing my parents to reject me. Harriete Lerner's The Dance of Anger has good stuff about "cut-offs" in family systems, which is what you seem to have with our mother, and ways to ameliorate them rather than play into them. I guess on the basis of my experience, if I had a choice between pursuing my parents' attention and getting devastated again and again, or just "calling it quits," or certainly taking time off from pursuing a one-way relationship, I would definitely choose calling it quits. i did take quite a long break from pursuing a relationship with my father, which, oddly, caused him a lot of pain and led to him pursuing me after years of complete neglect -- human nature is a weird thing! -- but anyway, I guess with both parents I did need a break, a period when I stopped pursuing them and trying to get their attention. I didn't have a child at the time or it would have been much harder, I'm sure. But over the long run, once I had given up all hope of my parents and I having the sort of close, supportive relationship I would ideally have liked, I did wind up with a closer relationship with them than I would have though possible -- regular phone calls, visits once or twice a year. I'm glad I made the effort to give up wanting more than they had to give, as it opened a connection of a sort between my mother and me that had never been possible, allowed me to accept what she did have, chilly and quiet though she was. I am glad that during the years she was dying of cancer, I was able to call her once a week to just let her know how I was doing and to hear how she was. I was with her when she died -- and at the time she went, I felt close to her. I know very well how disappointing very ill parents can be -- my mother was probably an untreated incest survivor and she had a life-pattern of picking mentally ill men on whom she became dependent. This was not fun for me, for sure, but I certainly couldn't change it. Finding what I could do, how I could be in touch with her as much as possible without getting hurt by her seeming indifference or by the sick men around her, was a worthwhile investment. I'm sure there are parents who are so sick that it just isn't possible to have any connection with them, although I can't imagine anyone so sick that one can't send a card once in awhile, send pictures of the kids and good wishes. Certainly, if you pray, no one is too sick to pray for. My favorite line on hurtful behavior from others, whoever they are, comes from some 12 step literature which advises that when someone hurts me, I should say to my Higher Power "God, this is a sick and damaged human being who, like me, presumably did not set out in life to be so."
Best wishes -- I really do know this hurts -- good luck also finding a healthy balance with your own kids -- I feel that I over-mother and over-nurture (and under-discipline) my daughter because my mother's distance and hostility were so awful for me as a child. At the moment, that is the hardest remnant of parental rejection in my own life.
M.