I totally understand how you are feeling, as I went through the exact same emotions myself when our first GC came along. We've always had a great relationship with our son, DiL, and her parents but, unfortunately, I let my emotions run away with me, and started to compare the other GPs, and the time they spent with our GC, to us. I'm not proud to say that I became jealous and upset. Occasionally, not without reason, but that's another story.
I pulled my emotions into check, and I'm delighted to say that we all now have a great family relationship ... in-laws included. Take it from one who knows, it's completely natural for emotions to run high at times like this. However, I now realize that it's really not worth getting yourself so upset, or jealous over. I bitterly regret allowing myself to feel that way.
You'll have years to forge a relationship with your lovely grandchild, so let your son and DiL have time to settle into their new roles as parents, and just simply let them know that they can always ask for your help if they need you anytime. . just And, whenever you want to visit, always check with them first to make sure it's convenient, and if it isn't, just ask them to let you know when it would be.
Most importantly, never, ever compare yourselves to the other grandparents. I remember my own grandparents, who had completely different backgrounds, one set wealthy, the others poor but happy. I used to do completely different things with them, but I adored them all equally. And the same goes for my own children with their grandparents.