Will this power source and setup work?
The current you have marked for the motor is only correct if there is a short circuit instead of the motor.  That resistor will reduce the current and the voltage to the motor.
If there were 1.9A through the 4.7Ohm resistor, that would be 9V*1.9A=17Watts of power.  What resistor were you going to use for that?
Questions (1) and (2) also apply to that 10Ohm resistor you have feeding the Arduino.  You will have losses, the Arduino might not run, and that resistor will get hot and/or need to be made for higher power than the typical 1/4 Watt resistors you will have at hand.
Don't power your servo off the regulated 5V from the Arduino.  The servo can draw a lot of current and cause the Arduino processor to reboot or hang.  The garbage from the servo could (potentially) kill the processor.
Please tell me you aren't planning to use a 9Volt battery.  They don't last long when driving motors.  They also don't like to provide much current.  They are made for small current (like, less than 100mA) tasks like running a transistor radio.




Fixes:


Ditch the 10 and 4.7 Ohm resistors.
Power the servo from the 9Volts, or through a separate regulator.  DO NOT use the regulated 5V from the Arduino.
Either use a 9V powersupply, or a different battery to power your motors and the servo.