Calvinism teaches something like this: everything we do is predetermined, including having faith in God. This means we have no free will to choose faith.
Mainstream Christianity supports the existence of free will.
Back to the discussion. Pence, like Christians in general, knows he needs to enter not into temptation. So the right conclusion is that his practice of not being alone with women shows he is among the most trustworthy.
That is to say, your suggestion about not trusting Pence is about as wrong as it could possibly be.
Calvinism believes that mankind is inherently evil, born into sin. Constantly lives in sin and any expression of free will would be sinful, unless they are constantly seeking the grace of God.
Just like other religions, there are different opinions in different Calvinist sects.
Having to have your wife with you at all times while conducting business might be practical and prudent for say Priests and Ministers, but the reasoning behind it as expressed by the OP is not what I look for in a President or somebody one heartbeat away from becoming President.