The aux pump does not directly affect the operation of the monovalve, it simply circulates more coolant to the heater core to give you decent heat at an idle. From what you've described, it sounds like your monovalve is the problem (try a rebuild kit). However, that does not rule out additional problems, including the push button unit. A seized aux pump can also cause damage to the push button unit, so you should either replace it or unplug it.