luggage space on the return won't be an issue even if you do pick up a lot of keepsakes,
unless you intend to take back your used diapers. (unlikely!)
The "ship to hotel" is a good idea, it insures you can send adequate supplies and you can even call them up a few days before your flight to confirm they arrived. Make sure to notify them well in advance and have your package marked heavily so they know what to do with it when it arrives. (they'll store it until you get there) If you call a few days before your flight and they don't have it yet, you know you're going to have to fall back to Plan B and pack diapers, otherwise you know there's crinkly goodness waiting for you when you arrive.
It also can save you from the airlines' retarded extra baggage fees etc.
As for how much... as many times as I've traveled I've
never felt I brought too many diapers. In
most cases I'm having to plan out my last few days and return trip home to make sure I have enough diapers to last. Always take more than you expect, because the unexpected
will happen. Diapers will get caught in zippers, you'll need to change unexpectedly a few times like at 3am when you had too much to drink the previous night and are about to leak
Pack the thickest diapers you have for overnight, with a few spares, and pack a good variety for daytime. You may find that diapers you expected would work well for the beach don't for some reason. Too hot, too bulky, not durable enough, etc. If you're not usually super-active at home, you'll find that diapers quickly fall apart when you've been walking around all day, and you'll go through at least double the number you normally do. If you're going to ship a box of diapers out, you might just plain go with huge overkill and then ship back any diapers you don't use. (if it's worth it, or just dispose of them when you leave) Vacation is
not the time to be stressing over needing to ration your diapers. If you're counting how many you need and plan to only pack that many, you're already setting yourself up for disaster.
I personally wouldn't pack ANY regular underwear, just to underscore the point that yes, you
will be diapered 24/7 all week
Finally, your skin may not appreciate the change in habit, so make sure you pack skin-care products - lotion, powders, AF, desitin, etc, whatever you find works well when your skin gets a little irritated, because the risk will be higher.
Enjoy your vacation! Take lots of pictures!