You cannot parallel part of the circuit without paralleling the other corresponding parts of the circuit.
post the schematic of your motor shield and tell us what pins you connected together using the signal or pin names from the datasheet. Post a link to a vendor that sells that shield so we can look at the photo.
When I'm programming this, do I need to program both channels to get the full 4A out, or will the motor shield pull the 4A on its own as it needs if I just program one channel?
Read your question again several times while looking at the schematic and see if you can explain to us how what your are suggesting could be possible.....