I was the sole grandparent for eight of my ten grandchildren, but then my daughter , who had four children already, married a wonderful young man and has two more children with him. His parents were incredible, accepting their four step-grandchildren whole-heartedly. Far from being jealous I was delighted that my gc had somebody else to love and cherish them. The in-laws lived in the same village and eventually moved next door to my DD, but they never interfered and were just very loving and helpful. Sadly, my DDs mother-in-law is now in a care home, suffering from dementia. She does not know that they now live in New Zealand.
I was present at the births of two of that daughter's children (without the father, who preferrred to be out somewhere) and one of my other daughter's four births. That daughter's MIL was a total nightmare, who considered her not good enough for her precious son and did everything she could to wreck the marriage.
Like my own ex-husband, she has never shown any interest in the gc, or bought them so much as a rattle.
I don't have any sons, but my sister has four, and has a good relationship with only one DIL but unfortunately that couple live in Scotland and my sister lives in Manchester and does not drive. However, they send her the plane fare every couple of months and we both spent Christmas with them and her DIL's family. Another DIL was very off-hand with her own mother and did not want her present at the births either, so my sister did not feel so excluded. However, those two grandsons are now 21 and 19 and often call to see their paternal grandmother.
I don't think there are any rules - every person, every family, every relationship is different. What is most important is not to view grandparenting as a competition - the gc need as many loving adults in their lives as possible. Normally, it will be natural for a young mother to want her own mother close when she has a baby, but that does not mean that her MIL will be less important in the children's lives.