The robot has 4 wheels, rear are driven by 2 separate motors on independent shafts, front are 2 wheels on a common shaft. Would this steer properly?

 

No. The front wheels would skid.

 

No........
The Front-Wheels must be "Casters" so that they can swivel in any direction.
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And should be the back wheels. Pushing something with castors in front does not work well.