You don't have to make your park reservation through your hotel reservation. It's just that, when the parks get busy, if the usual reservation "bucket" doesn't have any availability, hotel guests can use the bucket that Cruisehopeful mentioned to still get a reservation. (Then there are buckets for Magic Key holders, too, but I don't think those are relevant in the OP's case.)
Also, what do yoiu mean by a "three-week window"? Park reservations are only available to hotel guests during the period you're at the hotel.