Can mecanum wheels be mounted on carts that are linked together in a “train”? I am not familiar with all the possible applications of these wheels.
I am concerned that as the robot pulling the train of carts rotates, say 180°, the carts will not follow the arc of the robot path and start to slide/strafe sideways.
Do you mean that all the cars of the train have the mecanum wheels or only the leading one?
If you want the whole train to have the ability to move to every direction (including side to side, not just rotate) all cars will have to use these wheels, or perhaps just the leading one and the others omniwheels. You can find more information on how these wheels work at these links:
Mecanum wheels are meant to be used in mirrored pairs, so if you add a passive degree of freedom in between the front pair and rear pair, they won’t behave properly (have not seen the design itself to give an idea of what might happen). It sounds like you might prefer using wheels which can rotate individually, like: