[awelliott]

Let's get back to your reference: Mt 19:9 And I say unto you, Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery. In reading this, if you are the one who slept with your “non-wife,” you committed adultery at that very time. Jesus is saying here that if you didn't sleep with a “non-wife,” but divorce your current wife to marry another and marry her and sleep with her, you commit adultery at that time.

So far, so good, assuming that my wife, in your example, did not commit adultery...

Jesus further states that, due to the vow the married woman had with the husband who left her, whoever marries this poor lady (who may not have ever slept with another), will force her to commit adultery when they have sex with her (while the prior adulterous husband is alive).

Here's where we part ways. If the put-away wife has an adulterous husband, then Jesus' teaching in Mt 19:9 clearly states that she is free to remarry. If the husband has not committed adultery, then neither he nor the wife is free to remarry; Scripture teaches, as you correctly say, that they must reconcile or remain single.

[ConservativeMind]

We, perhaps wrongly, vow, “until death do us part.”

If you did this (I did), we are vow/covenanted until death.

You are never “relieved” from your vows.