I agree with Dan. One of the big reasons for doing this is that you will then have the stroller 24/7 so your daughter(s) won't have to wait until inside the park to be in the stroller and won't have to leave the stroller inside the park at the end of the day. Offsite places will deliver to your resort (even offsite resorts) and pick up after you are done with it.
However, if you do rent from Disney and park hop, keep your receipt as you only pay once for a stroller for that day.