What happens if you manually turn a moving DC motor the opposite way
As you are trying to add a torque to your steering wheel, to resist the motion, this means you should consider current-feeding the motor. You can control the torque by controlling the current.

A motor (a DC brushed motor at least) is a sort of transformer between electrical and mechanical domains. Voltage maps to speed, and current maps to torque (both with losses of course).

If you supply a voltage from a battery, then the motor will try to run at constant speed, more or less independantly of the torque needed for that. If you try to stop or reverse it manually, then it will try to draw whatever current is needed to continue running at that speed. The high current could heat the motor to the point of damage, unless the power supply limits the current.

If you supply a current from a current source, then the motor will try to deliver a constant torque, at any speed, including standstill. If that torque is enough to overcome friction, then the motor will accelerate to a speed which is in practice limited by the current source's maximum voltage, or the increase in friction and air-resistance of the motor.

Because you are controlling the current, you are controlling the power dissipation in the motor windings, the \$I^2R\$. Choose a low enough current, and the motor can sit stalled or be turned backwards without damage or overheating, while still delivering the constant torque determined by the current. That's always assuming there's no mechanical reason why the motor can't be turned backwards, like a worm gear on the shaft.

This mode of operation is called using it as a torque motor. There are special types of motor optimised for this operation, with better cooling when stationary (no air being stirred around) and lower cogging, but all DC brushed motors can work like this.