Spinning two wheels at the same speed

I’m building a car and I have an idea to power each wheel with another wired wheel. That means I want 4 wheels vertically to the ground and 4 horizontally… and I want them to spin at the same speed. The 4 wired wheels would be lying on the floor and to control the speed, I would control these wheels. The actual wheels of the car (the ones on the sides) would be somehow connected to those wired wheels so that they spin at the same speed. Therefore, by controlling the speed of the wired wheels on the floor, I control the speed of the wheels of the car.

And that’s where I hit a problem. I thought it will just take some tinkering with the advanced ball socket tool. Unfortunately, it’s not that simple. I use the following settings for the wheels on the sides:

Xmin: -180
Xmax: 180
Ymin: -0.1
Ymax: 0.1
Zmin: -0.1
Zmax: 0.1

The free movement box is ticked.

I apply those settings to the wheels and the floor of the car (main prop) so the wheels only spin around the X axis (therefore the car can go forward or backwards). The movement is handled by an elastic-based suspension.

If I apply those settings to a wired wheel set also vertically, I get the desired result: the wheel of the car spins accordingly to the wired wheel. Problem is, I need that wired wheel set horizontally, like the floor. Otherwise the other stuff I need to put into the car won’t fit. And it won’t look so cool. Trying to do that with the ball socket fails every time because no matter what the setting, some axis is always locked therefore blocking the spin.

Any ideas how to do it?