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.
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.