Popes at the time often had mistresses, sometimes several mistresses. That usually was quite public, in fact.
When you talk about a papal army in that period, what does that mean?
Popes raised armies just like any other head of state would do. But they often relied on mercenaries...at the time, to hire troops from outside one’s own country was done frequently....The famous Swiss guards that still exist at the Vatican, they go right back to Julius II...they’re both ceremonial at the Vatican today but they are also an actual police force.