My own biological father is married to one woman, (separated for 7 years now) and lives with another, yet he claims to be "Christian".
I have confronted him about this in the past and all I get is excuses, like if he divorces and marries his current girlfriend she will loose her SSI widows benefits, oh and "I can't afford a lawyer", I found him one real cheap tho, no contest, $325 dollars, even offered to pay for half of it, to no avail, he claims he can't afford it, yet you will find him every FRi on payday at the local pub.
I gave him this scripture, Matthew 6:24.
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The problem here is not that you should not judge your father (and you shouldn't, but that's another story), but that you shouldn't judge superficially, or let your own personal involvement cloud your judgement.
Real judges dismiss themselves from cases like this because "conflicting interests".
To deal with this case fairly, you need to go back 400 years, when Erasmus during the Reformation changed the basic rules of "marriage" drastically for the first time in 1600 years. Since that time, it has been a slippery slope, redefining marriage, divorce, and Christian status for the last 400 years.
At this point in time, only 1 out of 1000 "marriages" today could possibly be legitimate according to the Holy Scriptures and the teachings of the Bible.
The rest of all these "marriages" are illegitimate in the first place.
Was your dad or mom a virgin when the got married in the first place? No? Well then guess what: their "marriage" is Biblically invalid. They had previous obligations by God's law, and if you and they don't recognise that, or you don't believe in those legal definitions and values anyway, you've got no case for him "divorcing" one party and "remarrying" another.
All these actions are illegal and wrong. You insisting that he "remarry" avoids the obvious fact that his first marriage isn't a real Biblical marriage at all, and his second isn't either.
You'd be better off joining the Mormons and accepting polygamy under the circumstances, because none of these ad-hoc, make-believe "make your own rules" style "marriages" have any credibility with God or the Bible.
Most modern North American "marriages" are absurd, not just invalid. They are the erratic behaviours of compulsive liars and self-deniers and confused fornicators and adulterers. They have no meaning with God or the Bible.
Its like this: Imagine you come to a meeting in a den of thieves, and some are arguing about a few coins that one stole from the other, which he had stolen from a third bandit. Would God really step in and say, "Oh yes, those coins belong to you."
I think not. He would instead say, "Return ALL this stolen property right now, and never steal again!"
That is the proper solution to all these phoney illegitimate "marriages". Repentance.
Peace
Nazaroo