Did you connect the ground pins of both supplies together and did you connect all the ground pins of the L293D? My best guess is one of the ground pin either wasn't connected or had a poor connection so current flowing in one direction was blocked, but in the other direction it flowed freely.
When using separate power supplies you almost always want to connect the ground pins of both supplies together. The only time you will normally not connect the grounds is when you are isolating your low voltage circuit and people from the high voltage side. Normally this would be done using opto-isolators. There are other circumstances but they are not normal for the kinds of circuits on this forum.
There is no reason you shouldn't be able to power the Pro Mini and VCC1 of the driver by one supply and VCC2 with a different supply.