Driving through my neighborhood I stumbled across a sight that many before me have seen. A Power Wheel on the side of the road with a sign reading "Free". Many parents either received these large toys free from relatives and are then stuck with them after their child outgrows them, or worse the battery or charger die and as these are super simple devices you cannot check which passed without a multimeter and battery tester. The replacement cost of both is high enough to warrant giving the toy away.
Thankfully these toys are incredibly simple. Their design has not changed much since the 80s-90s. They have no complicated electronics and in fact are a few switches, a relay, and a few passive components to drive a motor. There are no processors here. What is in there is easily purchased off the shelf from any electronics retailer with the exception of the battery and charger.
Now the battery is nothing special. It's just a standard AGM lead acid battery you can buy off the shelf at any hardware store. The difference is that the toy manufacturers have put the battery in a custom sealed plastic enclosure, and attached custom leads to the battery with a quick disconnect that is fairly proprietary. They use a matching connector on the charger which isn't some super complex battery charger, but a dead simple analog lead acid float charger similar to what you can get from harbor freight. The trick is that custom plug.
Now you could simply chop out all of those proprietary connectors from the Power Wheel and install standard anderson or xt battery terminals, and just get a off the shelf AGM battery. Heck you could get a bigger battery. Most Power Wheels have space for a much bigger battery than they come with. Just match the voltage. However there is a much more modern, much easier upgrade you can do that is dead simple and super cheap if you're someone who has battery operated tools. Swap that weak lead acid battery for a Lithium power tool battery.
Head to amazon and search for "<insert your brand of tool> battery adapter". For me it's Ryobi. A quick amazon search turns up this kit that doesn't even need you to know how to solder wire. Just strip a bit of wire and use the provided wire junction matching red to red, black to black.
Here's Ryobi
https://amzn.to/3yDKA9X
Here's DeWalt
https://amzn.to/3iERCp2
Here's Milwaukee
https://amzn.to/3sfD7vd
Here's Ridgid
https://amzn.to/3s9rfe9
For a 12v Power Wheel you can just run it off the battery directly. The voltage increase won't blow up anything. You'll notice the Power Wheel will have a hell of a lot more power than it originally did. The low gear will have more power than the high used to with the original lead acid.
Now if you have a 6v Power Wheel, or if you find the speed is just too much you may want to put a speed controller like this in your toy to enable you to dial it back a bit. The speed controller effectively limits the voltage to the motor. So your 18v battery will drive as low as 7v
https://amzn.to/3fTtIVi
Through out all of this I'm assuming you have some existing cordless power tools. If not here is a good kit that is just a Ryobi compatible battery and charger.
https://amzn.to/3fQIQmo
Another benefit here is you can swap batteries on the fly. No more running out of power and have a sad child while they wait until tomorrow for that battery to charge. Ryobi batteries charge in under an hour in most cases, and you can keep multiple around. Swap the battery and your child is back off to the races!