There isn't an easy way.
Normally, I would recommend taking a cab, but in this situation, that's going to mean lugging the car seats around.
The best option (and it's not a good one) using Disney transportation is to be at the bus stop at 6:30, take the first bus to MK, and then walk to Chef Mickey's. They'll be late.
They could also rent a car.
If it were me, I would cancel the reservation. I probably wouldn't go to that kind of trouble for a good restaurant - I certainly wouldn't do it for Chef Mickey's.