Congratulations on grandmahood. It's a good sign that you recognize he isn't your baby. You sound lovely and well-intentioned. I don't know if a perspective from the other side (mother of the first grandchild on both sides) would be helpful? If not, please disregard.
@Luckygirl is a very wise woman. Years later, I still remember there were two times my mother visited during the first few months when, instead of holding my baby, she cleaned my house. It was so appreciated. In contrast, I remember when other grandparents would practically shove us out of the way to get to the baby. Anytime we tried to parent our own child, they hovered, questioned everything we did, and interfered. Their visits were all about themselves getting a grandchild, like a shiny new toy, and nothing to do with being truly supportive to either us or Dd. I dreaded their visits, sadly, and our relationship with them never recovered. I wish I could've told them that DH and I needed them more than ever, but not in the way they wanted to be needed. We did not need anyone to take over our baby. Instead, we needed support so we could learn to take care of our own baby. To this day, they still struggle with backing off, and accepting that Dd is not "theirs". Their possessiveness and overbearingness with Dd has led to us having a much more emotionally distanced relationship with them than I ever imagined. And that includes Dd's relationship with them. Thankfully, I don't think this will happen to you, as you are actively restraining yourself from the problematic behavior I described. Good for you for having that insight. Rest assured, it will pay off , and I know the parents appreciate it :-)