with it can still be a far trek from the handicap parking lots to the park entrance especially MK. There are no pictures that would do this justice for you to see how far the park entrance would be from the handicap parking lot. You might want to try u-tube and see if anyone has a video about it. These handicap spots are up front and closest to the park entrance; however, it is dependent on how far down the aisle you need to park the car. As stated previously, an end part of the aisle closer to the park would be best. You are directed to a degree where to park; so, this may not be so easy to get an aisle space closer. What might help is your daughter could let you out at the closest place possible upfront of the handicap parking and then she could circle around to park. This would help a little, not a lot.
The suggestion to find a regular parking spot at the end of the aisle closest to the trams might help, but you need to get the stroller on and off the tram if you want to stay together which may be too much of a hardship. You could take the tram while your daughter walks with the kids, as another alternative, here. You would have to meet up later.
It sounds like it's you and your daughter as the only two adults. I vote for a double stroller (you can rent them) that your daugther will push and I honestly think you should still get an
ECV. You can rent an offsite rental
scooter (much cheaper than Disney park scooters) that's portable and with most cars you can fit it in the trunk (just get the right size for the car rental). I don't see you lasting very well with pushing a stroller. You do have to have enough room for a double stroller and scooter to fit in the car rental. You may have to bit the bullet and rent a scooter in the park. You walking and pushing a stroller could affect your park time which is valuable, too. You can easily walk 6 to 8 miles a day at the parks. There are some who do 12 miles a day. I'm not qualified to know if rental strollers have any harnesses or safety belts in them and if your 3 year old is an escape artist then that could present another set of problems. You may want to practice at a local zoo with everyone to see how you can last through the day or not pushing a stroller. Most zoos will still be smaller than Disney World.
If you are going to give the stroller pushing a try no matter what then I would strongly suggest alternating your activities in the parks between seeing shows, doing rides, watching parades and eating. That way you can catch a rest, here and there. Avoid long waiting times for rides. I think it would be better to skip the attraction then to be in a line for 45 minutes. You can get fastpass. If you are not acquainted with this it gives you quicker access to the more popular rides.
I'm not sure about your situation, but you may want and need a GAC (guest assitance card). With an autistic child it may be better to have access to alternate ride queues. This can be had at guest services of the parks. You get it once for your whole stay.