I have only one daughter. She has two children now. I have been blessed to witness the birth of each of my grandchildren and am bonded with both. When the first one was born my daughter and son-in-law wanted some time to learn how to care for a newborn without anyone watching and correcting them. They were and are both excellent parents. I was welcome to visit and get all the cuddling I wanted. I stayed long enough to tidy the house and such then I would go home and give them their privacy back. When my daughter needed sleep she called me to say so. When she went back to work I took all my vacation and spent each day with my granddaughter. When they came home from work I went home for the night. I have also been able to help with the 2nd grandchild. He is such a sweetie. They would have loved to have help from the other grandparents but it just wasn't an option. One set lives 10 hours away and another set has medical issues which prevents their helping.
What is the translation? Ask. Be prepared for the 'honesty' a pregnant female or new Mother is likely to give. Honor their wishes as much as you can. If you know your daughter is sleep deprived you might want to 'drop in' and let her get some good sleep. The lack of sufficient sleep seems to be the biggest challenge for the parents of a newborn. When you haven't slept in days you don't care if your saviour is your Mother or your Mother-in-law.
Good luck to each of you. Grandchildren are such a joy.