Writing with a DILs point of view here & cannot agree more with mishap
I very rarely respond to posts & considered letting this one go but felt compelled to reply hoping that the more people that point out you are being rather unreasonable will help you to understand.
The reason I think it's so important that you're very careful with the way you handle this situation is because my MIL sadly shared your opinion that she had a god given right to our new daughter (although admittedly, there were lots more issues on top of this). And this ultimately led to my husband deciding he no longer wanted his parents involved in any of our lives.
After a brief period of estrangement last year, I pressured my husband to reconsider and 'give her one more chance' hoping that she'd change her overbearing, demanding ways but sadly she didn't and eventually again my husband told them that we didn't want to have anymore contact with them. I do agree with him this time, although I still feel sad that my daughter is missing out on having the maximum number of people to love her in her life. My husband doesn't share my sadness and I very much doubt he will ever back down.
I tell you all this to try to help you see that this could easily all end badly if you don't tread very carefully, my mother in law I'm sure would never have believed her son would have gone through with 'cutting them out' but she pushed him too far for too long, so please do be careful.
As others have said, you are very lucky that you have been offered the opportunity to visit and spend quality time with your granddaughter.
You will alienate your son and his wife if all you ever do is try and get the baby 'to yourself' even if you find a way to pretend its for their benefit. There is something in you that kicks in if a person persistently tries to get your baby away from you all the time and you naturally go against that. You will make the parents feel like a means to an end. You do not need to get the baby alone to bond with her, you can do that easily in the company of her parents. If during this time you constantly try to monopolise her and complain or sulk when she is 'taken off you' etc you will find you stop getting invited round.
The overwhelming feeling my husband and I could never get over was why on earth my mother in law wanted to put our baby through the ordeal of separating her from us when she knew that the baby wasn't familiar with her. It is purely selfish and it does not show that you have the child's best interest at heart, only your own.
I could go into the whole daughters mother vs sons mother thing, but I think I've probably said enough for now, like mishap I do not mean to sound harsh.
I hope you can find a way to be happy with your son and his wife's wishes, and develop a good relationship with your granddaughter, grandparents are so important in a child's life.