What is the issue that you are trying to overcome? A normal ordinary open differential will have no issue with this. I have a suspicion what the issue is ...
Jack up the drive wheels of an ordinary vehicle with an open differential. Engine off, transmission in gear (if manual) or in park (if automatic), brakes off including the parking brake off if it's on the same set of wheels that you are doing this with. Spin one wheel forward with your hand. The one on the other side spins backwards.
Now, if you are attempting to turn so sharply that the vehicle's center of rotation is between the drive wheels, the problem that you will encounter is that there is so little mechanical advantage that applying torque to the differential carrier doesn't result in much net forward motion ...
Small riding lawnmowers and such vehicles deal with this by not using a differential at all ... they usually use a hydrostatic drive, basically a separate little hydraulic pump and motor for each wheel. On the small lawnmowers that use this, the other wheels are not steered, they are free-pivoting, and the steering is done by changing the displacement of the hydraulic pumps differently for each side. ("Skid-steer" construction vehicles work the same way.) Steering (and driving) is done using left and right joysticks, not a steering wheel ... the joystick is directly coupled to the mechanism that changes the displacement of the hydraulic pump (including reversing it.
If the real problem that you are attempting to solve is something other than what I just explained, then please clarify.
