Hi,
Below is a simplified diagram of your schematic, using a L293 will not do the job you need.
The problem is the Enable pins.
When enabled the outputs follow the inputs.
When not enabled the outputs are open circuit.
L293 has tri-state outputs.
But the enables control a pair of outputs.
If motorpin 1 and motorpin 3 need to be HIGH and LOW, both enable pins will need to be HIGH, however this means motorpin 4 is connected to an enabled output, not an open circuit that your motor will need.
I hope that makes sense.
Tom... 