As I understand it, what you get when you buy the hopper at check in, is an Ultimate Park Hopper, which is fine if you are planning to go to the parks on both your arrival and departure days. Since these tickets are tied to your reservation, the only other option here, is to have 2 or 3 separate reservations, one each for your check in and check out dates, and a third for the days you will go to the parks. Put the hopper tickets only on the portion of your reservation when you will be touring.
Can't help with the Alamo ticket cancellation fees, but there is usually no cancellation fee from any of the car rental companies. I think it would be odd if they do.
Have a great trip.