Such an interesting thread and I'm reading with a tiny bit of trepidation.
I've recently became a GM for the first time this weekend 
My DS and DIL have had a short relationship, under one year, but are devoted to each other and make each other so happy.
I have taken a great interest in my DIL pregnancy as I am genuinely interested in her and as I work as a midwife even more so as I am well aware of all the problems that can occur in pregnancy and labour.
I was invited to visit a few hours after the birth. I took supplies of food and drink in as requested. The first person I went to as I entered the room was my DIL to give her a hug and tell her how bloody marvellous she was as had been in latent stage for 48 hrs and we had shared multiple texts giving advice and offering support. That woman is amazing.
I then asked if I could cuddle my GC and it was just perfect I love him as if he has always been here. My DS and DIL have made their own beautiful family now of which I am honoured to be a part of.
I was honoured to be asked to collect them from the hospital to take them home. She has texted me in the middle of the night re feeding and I have offered advice and all seems to be going ok so far.
I will wait to see when they wish to visit us as they live with her parents and I would never ever put pressure on her to bring baby for a visit to our house as she needs to rest and feel comfortable.
They know where we are day or night and we will be there in a heartbeat for them but this is there time settling in as a family getting to know their baby and adjusting to a new life.
I am certainly not jealous that her parents are seeing the new GC why would I??
I am happy in the knowledge that this baby is so loved by so many and, I'm sure it will make our times together all the more special.
A new baby is a miracle the ultimate celebration of life. The new parents need time to adjust to this quite overwhelming event.
We have the rest of our lives to grandparents.