Since I was a flight engineer, and later F/O on the DC-10, let me help;
To start - the three hydraulic systems are completely
separate from each other. As said before, the reason the United DC-10 lost it all was because the exploding engine took out all three lines in the tail. And after that accident, a retrofit put valves in the #3 system forward of the tail engine to prevent that sort of thing from happening again.
The #2 hydraulic system on the DC-10 is powered from the tail engine, and is actually the least busy of the three. All control surfaces have redundant power, and the only thing (for the most part) the #2 system drives are parts of the rudder, elevator, ailerons, flaps, and spoilers. The #1 and #3 systems also drive the landing gear, steering, braking, slats, some flaps, and the stab trim, in addition to the control surfaces.
The #2 system does power a backup non-reversible motor-pump, that provides pressure (but not fluid) to parts of the #1 system in case the #1 engine pumps give out (stab trim & rudder).
So in short - no. The loss of the tail engine does not appreciable affect the hydraulics on the DC-10. In fact, the loss of one system is treated as an abnormal procedure. Only if you lose two systems does it become an emergency. And finally, the hydraulic pumps are driven off the accessory drive from the N2
section of the engine. If the engine quits because of a fuel problem or something else that allows the engine to windmill, you'll still have hydraulic pressure in that system as the rotation of the engine keeps the pumps working.
One smooth landing is skill. Two in a row is luck. Three in a row and someone is lying.