Off the shelf...
The rear end, what is it out of?
Is it a limited slip?
Why does it not just pull on one side and constantly try to turn one way or the other?
I am contemplating building a rig, similiar to an otter/thiokol imp/ranger but the third member is a sticking point for me.
The drive sprocket is a sticking point also, but that is just a question of how much the war dept. will not know, I mean, will allow me to spend.
Let's start at the front. The engine is an big old single cylinder Kohler. A more modern V would be better. You want good torque, turns are very demanding of the engine. The clutch is automotive type. There is a small 3 speed gear box. The drive shaft goes through a shield to the differential in the rear. Differential output goes to each side, of course. There are external support bearings and a drum brake mounted. It is just mechanical with long arms going to driver up front. There is a custom chain box to compensate for auto size drive tire. These are snow tires that engage the tire guides on the track, more or less. The drive wheel uses what appears to be the hub from a rear wheel drive car. Those pull straight out with shaft attached, making it easy to adapt to this use. Non-driven wheels use trailer spindles, hubs, and wheels. Track is 2 conveyer belts held together with straight angle iron grousers outside and wheel guides/backing plates inside.
As to all the power going to just one side, that only happens if other side is freely spinning. And tracks do not like to spin. Turns are done by changing drive ratio between sides. Brake steering converts one sides drive to heat making it move slower. Controlled differential, like older Bombardiers, create a gear ratio difference between the sides. Hydraulic drive sends more flow to one side to turn. Because flow adjustment is infinite you make very tight turns. If the control valve includes reversing then you can turn in place. Neat, but VERY hard on the track.
If I were doing one like the Ranger I'd start with a good garden tractor, like an old Cub Cadet. They are the only one's with drive shaft. My perference would be hydrostatic drive, makes it much easier mechanically. Especially as CC puts hydrostatic drive and differential in same case. The brake discs are mounted on the differential output, so easy to incorporate for steering. The rest is custom chain drive for proper ratio and support.
Personally I don't like brake steeing, it wastes power, you have to keep the engine at fairly high rpms and it needs to have a governor. If I were doing it I would go with hydraulic pumps, controls, and motors driving sprockets. Surplus hydraulic pumps and drives from zero turn radius mowers is an idea. But they are too weak for any serious use. Adjustable volume pumps are nice but expensive. You can use a fixed pump with flow control valve. These can be found where the unneeded flow is dumped into a return line. Use one drive motor for each side. If you do the all the ratios right no mechanical gearing needed. Best to have each side independant. Two pump sections bolted together is best, just like used on skid steers. They bolt directly to the engine with a mount adapter. Sprockets can be purchased off the shelf, heavy castors or wheels support the track. Bombardier rubber support wheels are the simplest and completely of the shelf.
I still want to build one of my own, but just don't have the time.
Check out Surplus Center for cheap parts.