A current consumption of 10mA is not enough to get anything hot.
You should not measure the current consumption by breaking the ground because this causes what is known as "ground lift". This is where the ground connection on various parts of the board are at different voltage levels. This can interfere will the proper operation of the circuit.
What is more, during the setup of this measurement then it is possible that there is no ground at all connected and then you can get parasitic grounds happening. That is where ground currents can flow through signal pins and damage them.
Does the driver that gets hot, gets hot in any of the four positions? Or is it only one position where it gets hot? As I said 10mA is not enough to get anything hot so you must be missing some large amount of current flowing through something.
It could mean that, but it could also mean a fault on the shield board. You are better testing for that with all power off, all boards separate and a resistance meter.
I am assuming you are still having problems with the Uno's power regulator overheating?