You are so lucky to have a mother you can grieve for. My feeling when my mother died was one of relief, but I won’t go into that as I only mentioned it to make the point that you obviously had a lovely mum.
But, she would not want you to feel that her death overshadowed the birth of her great grandsons. Yes, I understand anniversaries are especially hard, but as someone who has had to deal with a recent tragedy myself, can I make a suggestion?
Allow yourself the morning of her anniversary to grieve deeply. Visit her grave, or whatever. Listen to her favourite music. Look at photographs. Then when you feel ready pick yourself up, give yourself a mental rub down and turn on to your grandsons’ birthday.
It works for me. It might not for you.