The circuit as drawn seems correct. However there ought to be some decoupling on VCC1 of the SN754410 near that chip.
When interfacing to a higher-voltage driver chip like this it is a wise precaution to add some series resistance to each logic line - a few kohms will help protect the Arduino from any over-voltage.
A typical failure mode goes like this:
- Something stresses the motor driver chip beyond its limits (voltage, current, power...)
- That chip then melts/shorts/whatever
- All its inputs connect to some common voltage, if unlucky this will be Vcc2 (12V)
- The 12V on the logic lines fries the microcontroller.
Adding series resistors should prevent 3) leading to 4)...
I note you are using a lead-acid 12V accumulator without a fuse or other current-limitation device - not wise.