I don't know the answer but I will take a guess.

These mobility scooters use a lot of electronics. Switch mode power supplies are a way of controlling a dc motor more efficiently than with rheostats or the solid state equivalent, large power transistors. There are also electronics and relays to change the polarity for reversing and further electronics to prevent the scooter being able to reverse as fast as it goes forward.

When two motors are used they could share some of the same electronics or the electronics could be duplicated for each motor. While this would provide a fairly basic control there are some considerations, namely the front wheels travel further than the back when going around corners and during this the rear motor will be pushing the front motor and it will be acting as a generator.

The circuitry has a lot to do as apart from controlling each motor it must synchronise them so they consistently produce the same effort and at the same time allow the front motor to speed up slightly when cornering so the rear motor doesn't have to push it.

Clearly it is a requirement the two motors must talk to each other via the circuitry. While it would be better that each motor provides torque feedback, such a system would be complex and expensive and so it is more likely the current each motor consumes is monitored and synchronised via intelligent circuitry.

From your description I suspect the problem is a breakdown in communication between the two motors or the current monitoring or the synchronisation circuitry.
Usually scooter manufacturers assemble all the circuitry on a single board and seem reluctant to offer a checking and repair service, preferring instead to sell complete boards at inflated prices.

Double checking all the connections might produce results but the chances are you won't be able to go much further without a complete circuit diagram.