Arduino Power Wheels Wild Thing conversion project

So I bought my son a Power Wheels Wild Thing, which drives like a zero turn mower. It has two big 14" wheels and a smaller castor wheel on the back. It's pretty neat. Anyways I can adjust the speed via two very poor made buttons that can cycle through 4 different speeds. I normally like to keep it slower when he's driving in my apt complex parking lot and near cars. But when we make it to the walking trail I let him go full speed since he has more room to maneuver. In order to change the speed he has to unbuckle, stand up and take the seat off so I can set the speed. I'd love to be able to control this function remotely. That in addition to the input from the joysticks have severe lag going to the motors. It'll continue for a quarter of a second or so after the joystick is released or adjusted, which makes fine adjustments in steering nearly impossible. Also I would like to be able to control the Power Wheels remotely from my phone, for when I need to move it for whatever reason.

The Power Wheels currently has a circuit board and the inputs from the joysticks are either 4 or 5 wires if I remember correctly, so I think I should still be able to use them with the Arduino board as an analog input.

Does this sound like something a newbie could do as a summer project? The sooner the better, but I wanna be realistic. I guess I should also ask if this would be possible, I feel like it should be fairly straight foreword but I honestly have no idea.

I also have never written an app for a phone either, but feel a simple app should be all that is needed, therefore simpler.

Any suggestions or comments?

Here's a link to the Power Wheels for those who are interested

Power Wheels Wild Thing

IV_Explorations:
Any suggestions or comments?

Yes. Do not attempt to make a remote control device that will carry your child.

Much of the rest of your ideas look good. That one does not.

vinceherman:
Yes. Do not attempt to make a remote control device that will carry your child.

Much of the rest of your ideas look good. That one does not.

First off, why not? Second I'm not gonna sit him in it and not allow him to drive it. Where's the fun it that?

I plan on making it remote control so if he feels like walking I can drive it around with my phone. Also I want to be able to adjust the speed limit via my phone. That way when we are around stuff he can hit I can slow it down, but as soon as we are clear of obstacles, then I can open it up without having to take the seat off to adjust the speed via the factory board