henrydog, firstly don't worry about the hand-stamp washing off in the pool - it won't.
My advice is to make the most of the flexibility of having the 10 day passes - if they have cost you the same as the 5 day ones, then think of it as having 5 days for free and don't feel that you've got to get 16 Disney hours out of each of the 10 days to have got your money's worth. I know this has been said before, but I think it's worth repeating because I know it's an easy thing to do.
In other words, because you have got the 10 days, you probably won't need to spend <i>whole</i> days at Disney. You could have some days where you arrive at a park at the opening time, spend 5 hours there, then go back to your hotel for a swim, or go shopping and then go back to a park during the evening. Or get up later, go shopping or to a water park, back to the hotel and then a park during the evening. Obviously there are hundreds of possible combinations. The thing is that you make a broad itinerary, but you can't (and wouldn't want to) plan for every eventuality. You don't know what you will feel like on any given day, and we often deviate from the plan. I know from experience that spending all day and all evening in a park doesn't work for me - but I didn't know that on our first trip.
<b>Definitely</b> do Universal Studios and Islands of Adventure. IMHO, Universal Florida with the two parks and CityWalk is every bit as good as Disney. Sea World is a nice change from the theme parks and worth a visit if you can fit it in, although I would be tempted to wait and see and buy a ticket at the gate if you decide to go for it. Busch Gardens is a great park, but there is <b>so</b> much else to see and do in Orlando that I think an 1.5 drive (each way) to do it is overkill for a first trip. I never tire of the WDW and US parks - there are still things I haven't seen in 6 trips - and I would recommend you spend days revisiting (especially as you have the 10 day passes) rather than try to fit in BG. JMHO. Again I would suggest reserving judgement until you are there.
The best piece of advice I can give you is to make sure you take time to take it all in. On our first trip we blitzed from ride to ride, ticking off the attractions as we went. You miss so much if you do it this way - the theming of the parks is incredible and is what sets them apart from anywhere else you will have ever been. Soak it all up, live every minute, otherwise you will get home and it will all be a blur - a happy blur, but a blur nonetheless!