When you check the motor connector, you should see two pins with a resistance between them of 1.24 ohms. The other two pins should show the same resistance. There should be infinite resistance between the two pairs.
When connecting to your driver, the polarity of the winding pairs are of no immediate concern. If you've got them wrong, the only thing that will happen is that the motor will step in the wrong direction, and you can fix that simply by reversing the connection of 1 pair.
If the driver is getting hot, there is probably something wrong with it. To check:
1 - get 6 ea, two watt, 5-ohm resistors. Connect them by twisting their leads together so as to make two 3-resistor assemblies, each with 3 resistors in parallel.
2 - Connect these two resistor bundles to the driver, with one set going from a+ to a-, and the other from b+ to b-.
3 - Apply power. The resistors should get very hot, but not the driver. You should see about 3 volts (technically, 2.7) across each resistor. Stepping the controller should cause the voltage across the resistors to reverse polarity, but not amplitude. Only one resistor should change polarity per step.
If you want to examine things over a long period, use 3-watt or 5-watt resistors instead of 2-watt. They will cost more but last longer. Don't bundle them too tightly, since you want air to be able to cool them.