Lizzie10, I don't think you're being overly sensitive. I think it's a natural thing for most grandparents to want to see their grandchildren as soon as possible after the birth. The fact that you don't live close by, and you won't be able to pop along to the hospital for a quick visit once baby arrives, is obviously making you feel a little left out. I totally understand how you feel, as my DS and his family live overseas, and the thought of having to wait for weeks to see my first GC, I found very upsetting. As it turned out, my DS & DiL did want us there straight away (obviously not at the birth!), although DiL's mum wasn't too happy about us arriving, but it wasn't her call! It all worked out in the end though!
All couples are different. Some love having visitors/family around, and some want their own time together without interference from anyone else. At the end of the day, you have to abide by what they want, and don't take anything personally. I'd suggest you speak to your DS and his partner, and tell them that you fully understand and appreciate their wishes to have time alone together when mum & baby go home. Just ask them if they would mind, when baby arrives, if you book into a B&B for 2 or 3 nights, so you can at least have the odd short visit to see your grandchild. You could always enjoy spending the extra time with your daughter whilst you're there ... and do a little baby shopping together! And then, once they are more settled into their routines, they perhaps wouldn't mind having you stay for the odd weekend so you can get to spend a little time with them and your GC.
Rest assured, in my experience, I've found that on subsequent visits, the new parents have been very welcoming, and more than willing to pass GC over to nannie & grandad so that they can have a rest! I come home exhausted, but I enjoy every moment of it!Lol
The worst thing you can do is to have disagreements, try to be easy going, even though you may feel a little left out. Just go with the flow, be guided by your DS and his partner, and enjoy being a grandparent.