Baby showers are hosted by friends of the mom-to-be, not the grandparents-to-be. (Otherwise, it looks like the grandparents are just trying to get gifts for the baby.) A shower is a get together party, so I don't see how that could be done online.
The best thing to do for out-of-town friends and family is to have a gift registry ready at a few stores that they can access online. (Don't mention the registry unless they ask; again, it looks greedy.) If they don't ask about a registry, you can mention baby room colors or themes, or sex of the baby, if they want suggestions.
If you want your daughter to be able to open gifts from the East Coast friends and family during her local shower, you can maybe have them delivered to the hostess of the shower. That way, they can be included during the party. Also, have someone at the party take still pictures and videos to send to you. Then, you and the East Coasters can gather together to watch the video and enjoy snacks and fellowship.