Servo twitches heavily while DC motor is running

Firstly you need proper power supply for motors and servos. a 9V battery (PP3 size)
is inadequate for any motor or servo, just give up using them. Something like 4 or 5
AA rechargables with decent multi-amp output current is where to start.

The jitter in the servo may be due to power rail noise, in which case a proper supply
will cure it.

Or it could be RFI, interference from the high currents in the motor leads inducing
signals in the servo wiring.

Ensure wires to motors are twisted pair, or even shielded. Keep wiring to motors
and servos well away from sensitive electronics and each other. Ensure you have
a star-ground configuration and that high-current ground paths are outside the
Arduino board itself. Small motors can have a small ceramic capacitor soldered
direct to the terminals to quench brush-arc noise, something like 0.1uF, which can
reduce RFI (especially true on small cheap motors with metal brushes).