OK, I have spent the last hour studying the wiring diagram. Link here:
http://www.onlycubcadets.net/forum/showthread.php?t=21
When you turn on the key to the run position, 12 volts is sent through the 15 amp fuse to the seat switch and the front and rear PTO clutch switches. The front PTO switch, when off, sends 12 volts through terminal B to E (the normally closed contacts of the relay) to the + side of the ignition coil. When the rear PTO switch is switched on, this energizes the relay and opens the contacts thus cutting power to the ignition coil. When you sit in the seat 12 volts is then restored to the ignition coil via the seat switch. This is why it will run when you sit in the seat.
You said you think the PTO is engaged while it's running and when you turn the rear PTO switch to on it causes the relay to squeal. I think your rear PTO switch is the problem. I think the contacts within the switch that energizes the rear PTO and the relay have welded themselves together thus keeping this circuit energized at all times while the key is turned on. Replace the rear PTO switch with a known good one and see if this solves the problem.
I hope this solves the problem with the ignition. The front PTO I feel is a completely different issue unless there is not enough power to fully energize both PTO's at the same time. I would replace the voltage regulator as suggested by John Hall.
Let's solve each issue one thing at a time.