Separating Arduino uno power from Arduino motor shield motor power

Help!!! My Son has a science project electric vehicle due and we have been fighting issues with separating the Arduino Uno's power from the Arduino's motor shield power for some weeks now. We have cut the "Vin connect" trace on the motor shield circuit board and put a dedicated 9vdc battery into the Uno's dedicated battery input. The motor shield has it's own dedicated 9vdc (6 each 1.5vdc AAA batteties) battery supply. And the the motor shield won't work. We can reconnect the motor shield circuit board trace (Vin connect) back up and the motor will run but not at peak performance. What are we doing wrong?!

Can you take a nice, focused pic of the setup? If you need to take more than one pic, that's fine.

How do you know that the motors are not working at peak performance when Vin is connected? From what I've read, this is the only time the motor works. According to the product page, you only need to cut the trace when using 12V or more. Since you are only using 9V, why did you cut it?

What motors are you using? A link to a datasheet or the product page is preferred.

We measured the current straight from battery supply to motor while running at 0.6 amp. Then ran through arduino system and took current reading. Current jumped to 2.5amp and rpms went down. We then did what we read online about cutting vin trace and put on two battery supplies and the motor wouldn't run. The motor and transaxle is off a cheap trashed RC car.