I did not anticipate just how much I would love my grandson. It's the greatest love I have ever known, my husband and his other grandparents agree
Sorry to pick up on what was probably just a turn of phrase - but really..."the greatest love" you've ever known? More than for your own children?
I'm a mother of four and grandmother of three and I adore my grandchildren. But it isn't by any means the greatest love - how could I say that when I have children of my own?
OP, it all depends on the relationship. As a PP has said, those of us who had our babies in the 70s had to fight to get out of hospital and visiting was strictly limited, so the baby was usually at least a week old before anyone visited at home. If grandparents were allowed to visit in hospital, it was for a brief time.
I also think you'll be bored witless if you do stay at home for two weeks (though I note you say "one or two") - as will your DD1 - I was always desperate to get out and about after the birth. Don't anticipate too many problems with your older child - keep things calm and keep her occupied and she'll be fine. There's not much bonding she can do with a new baby - just involve her if she's interested and don't worry too much if she isn't!
I'd say the thing to avoid - when possible - is sitting with the baby on you, hour after hour - let someone else hold her, or put her in a crib/sling so you have your hands free to do things with your elder daughter. If you're breastfeeding, you can easily read to your older child while you're sitting, or involve yourself in her games. She'll be fine.