When MOSFETs get hot, that usually means the gate voltage is too low. It looks like your driving the MOSFET gate through a resistor voltage divider. It would be better to drive the gate straight from the PI's GPIO pin. Also a flyback protection diode would be a very good idea.
Read up on flyback diodes. There are additionally numerous motor driver IC's specifically for this purpose.
A flyback is critical in anything involving a magnetic field, especially a collapsing magnetic field from a motor that stops spinning. The field collapse induces a relatively huge current which will be many many many times greater than anything a normal component is designed for.
Not having one is like driving your car down the highway without any breaks. The only way to stop is to crash.
> So your suggestion is actually introducing a second magnetic field, so now you've doubled the chances of blowing up your Pi and or the MOSFET.
No. You haven't fixed the original problem, but your motor is now isolated from the rest of the circuit.
You've just now have a relay with an inductive element instead of a motor. Ultimately, you haven't solved anything (unless you are using an AC motor, and you don't have a triac or something else solid state to control the motor). You still need the flyback diode.
But you haven't doubled your problem by introducing a relay, merely moved the issue to another part.
Now - in regards to the mosfet - many mosfets (not all!) have a built in protection diode between the source and drain. Check your datasheet for details (including what kind of back-feed voltage/current can be handled by them - some may need an added diode with better ratings in detail).
EDIT: Also - some relays have built-in protection diodes (or can be ordered as such) as well (again, check the datasheet). You see this more on relays for automotive applications (ie - standard BOSCH style relays) than ordinary bare PCB relays.