120v DC Agitator motor, 240v 5500w heating element
I'm not entirely clear how you've wired it up. Does the DC motor have its own speed controller (motor drive)? Or are you connecting the DC motor to the same adjustable power supply as the heating element?

It's probably fair to say that connecting both the heating element and motor to the same adjustable power supply is a bad idea - unless it's specifically designed to drive motors.

Is the DC motor's adjustable speed drive actually designed for running DC motors? If you use a simple "lamp dimmer" style power supply (like you'd use for a heating element) on a motor, you will get undesirable effects such as the motor stuck on full speed - or even damaging consequences. This happens due to the inductance of the motor. A proper motor drive is designed to cope with this.

If you're using a correct motor drive for the motor and a separate power supply for the heater, then this problem shouldn't occur. The fact it does tells me something is very wrong with the AC wiring. Perhaps there is a poor connection in the building's wiring allowing spikes to occur when the heater PWM switches on and off. This could upset the motor drive causing it to run full speed. Try using a long extension cord to connect the motor to a different outlet in the building. Does the problem persist? I would definitely recommend involving an electrician in this situation since poor connections could pose a fire risk.

As far as grounding goes, you really need to be sure that you're properly grounded. If necessary, run a separate ground wire for the installation to a place you know a decent ground is available. I don't think it will affect the performance of the motor much, but it could mean the matter between life and death. Most heating elements for liquids rely on a ground connection for essential safety. If you really can't get a ground connection, you need to run the heater from an isolation transformer. Unfortunately at 5500 watts, it will be a very large and expensive transformer. But how much value do you put on your life?