Increasing voltage to motors
I see what you are trying to do... The schematics turn out not to be quite as simple as you have drawn though.


Resistor between the battery and the PCB wont work since the current draw will likely vary a lot. Use a Linear Voltage Regulator, like the jelly-beans 7805.
Simply adding two transistors in front of the motor will not do the job either. I am sorry to tell you, but you need a circuit called H-Bridge. Please read through it.




The PCB most likely already implements such structures. Perhaps you are better-off plugging the stronger battery directly in and seeing if the thing explodes. I'd say you have a 50% chance of success.

Note that regular 9V batteries have quite significant internal resistance, so it may not run better at all. Try a two-cell Li-Po battery. These are much better, but require some attention when charging.