Yeah its horses for courses.
The R/C approach would allow you to do a much simpler conversion using standard RC components for the most part. Would get you up and hooning around the lawn fast just using plain old RC control before you move on to write custom firmware.
Getting jollies quickly is not a bad thing for a kids project (and of course one where any sort of manager is involved )
Kids will still see it as a fun project, they normally don't care about who wrote the firmware like we do
Arduino approach trades off development time for much more flexibility.
Yeah, my son doesn't really care about adding R/C. That feature is for me so I don't have to stay a few feet behind him to make sure he doesn't cause havoc. He's just happy to drive it. There's a lockout screw that enables 5 MPH (as opposed to 2.5 MPH) and I removed that and let him go full speed once. When he got to the other side of a field and decided not to come back is when I decided that 5 MPH will only be enabled again once the remote is set up - even if it's just controlling the throttle initially. Chasing after a toddler zooming around in a little Jeep is exhausting, and looks ridiculous.
So the R/C isn't for him. I think he'd be thrilled just having an ignition key that works. The R/C ride-on car we had had a plastic key that went into the ignition and when turned, the car turned on with headlights and an engine revving sound. This:
(click) is what the Power Wheels has. It doesn't even come out. Well, I yanked it out so I could find a functional replacement (still looking) but it doesn't do anything except sit there.
But at no point should the Jeep be non-functional, even while in the intermediate build stages. I'll either tie into the existing wiring, or run a secondary set of wiring that can be removed if needed.