Ok, good start. It's hard to get a good view of just how much room is under the rear seat.
To start, the original axle and gearbox would be removed. You will probably need a new axle or grind down the tabs on the old one so that it's uniform diameter. You will probably need to do some cutting to get the #7 power wheels gearbox to fit in the location of the original gearbox. Then do the same cutting on the other side to fit that gearbox. Mating the power wheels wheel drivers (I might suggest using the thinner Mustang drivers) with the wheels will also take some work. Sometimes the driver can be cut out to fit the wheel, then attached with some small screws.
Your 12v battery might need to be installed in a fabricated tray in the space behind the back bumper. You will want to use the power wheels gas pedal too. Just cut out the floor to fit the pedal wherever it interferes, making sure you have some meat left to secure it to. The gear shift will also be interesting. You may be able to just cut out a slot to fit the lever through and somehow secure the box to the inside of the tub in an appropriate location.
Or... You can use the original throttle pedal and shifter to trigger relays to control gas and fwd/rev. One way or another, it's gonna get messy before it gets better
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