Deanna, both my husband and I can speak on behalf of your children.
My grandmother made my mother's life very difficult. My mom was accused of stealing, being a bad mother, and more. To improve their life, my parents moved an hour away from my grandparents. With all this happening, my mom made sure that my dad and us kids visited frequently. My grandmother and I had a very special bond. When I grew up and realized the sacrifice my mom made on our behalf, I really came to admire her strength. As hurt as my mom felt, she would not allow the family to fall apart.
On the other hand, my husband's story is the opposite. His mom left her home at 16 and never looked back. Even though his grandparents lived 5 minutes away from his home, my husband never met them! His mother was approached many times by her mother-in-law about considering reconciliation for her children's sake. However, she would not hear of it. Now both of his grandparents are dead and gone. So goes a part of his history.
My grandmother past away just this past spring. Yes she had her faults. But I am so grateful to have had her in my life. She gave me wonderful stories, traditions and memories, things I can pass along to the next generations in our famiy.
My mother-in-law and I are not the best of friends, but my children adore her. I prefer to follow my mom's example and put up with her then to allow my children to lose the precious gift of a loving grandmother. That is what mothers do.