I would strongly recommend renting offsite, scooters can run out of availability prior to official park opening due to early entry guests. Also, the in park rentals are very difficult to maneuver and go VERY slow. Don't get me wrong, you shouldn't go faster than people walk, but babies can crawl faster than the park rentals go.
If they run out of power, they usually have a few in reserve that they can change them out for, but the batteries have been dying more and more frequently, so the likelyhood of being able to exchange them out late in the day drops constantly.
I know you said that renting offsite isn't a good option for this trip, perhaps if you let us know why not, we can assist in finding a way to make it a better option for you, as really if you are going to need it every day, offsite is the way to go, if for no other reason than price, but also because there is the very real possibility they will all be gone by the time you get to the park. When we were there last, they were selling out before park opening most of the time.