I have 3 DiLs and one SiL.
It's different for all of them
First DGC was far away but I still felt envious of her parents who were very close. I mentioned this once to the other DG and she said "we only have them when they are ill"
While the DGC were at nursery, they often seemed to be poorly.
NextDS is the other side of the world so they've had no DGP and I have only spent a few weeks with him in his life. He's 10.
Next DiL once asked me to look after DGD for a few hours once. We always offered but they said no yet they pay babysitters so I could really develop paranoia 
My DD lives 2 hours away so a bit far. I see them quite often and so does the other gran.
Their house is geared for children and there are 2 of them which makes a difference.
I hope you soon get to spend some time getting to know the baby.
It's an exciting time
Should I have been a better person?
Changing from a Manual car to an Automatic after driving manual for around 50 yrs
Support and friendship for those whose lives have been affected by estrangement.
but I'm sure we all understand how you feel