You say it is necessary to remove the jumper next to the terminal blocks when running external power to the shield.
That statement applies to the case of using separate supplies. It is not a good idea to have two power supplies connected in parallel.
If you have only one supply (presumably one that is compatible with both the motors and the Arduino), you can leave the jumper in place. The supply can be connected either to the Arduino DC jack or the external power terminals on the shield.
The Arduino is rated for 7-12v DC input, so it will work with your 12v supply. The other concern is possible electrical noise from the motors interfering with the Arduino. If you see any erratic behavior or resets on the Arduino, you should go to separate supplies.