First thank you for posting. Appreciated.
It is helpful to do two things regarding this topic.
1. look at all the complete teaching of Scripture regarding divorce, which Mark 10 does not wholly contain.
2. define who is who in the passages.
In the Mark 10 passage, written to a gentile audience, there is no exception clause stated for adultery
In the Matthew passages, written to a Jewish audience, further clarifies Moses' instructions regarding divorce. Christ says that only grievous sexual sin justifies breaking the marriage covenant and is the only reason to end a marriage.
When the complete words of Christ are tallied, there is only an exception for sexual sin.
The person who has been sinned against by his or her spouse does not commit adultery, but is the victim of adultery.
The marriage is not required to be ended, but can be ended after an adultery is committed. Christ does not say this person who ends a marriage because of adultery is committing adultery by remarrying.
In fact, there is no reason to end a marriage via divorce for adultery, if the divorce doesn't actually end the marriage. Is someone has been set free from a marriage, because adultery ended the marriage, then there is no restriction of marriage for an unmarried and free person.
This is very different than a divorce initiator - man or woman, divorcing apart from adultery - who marries another, and causes the his or her new spouse to commit adultery.
Given that theological papers and books have been written on the various view, there is no way we can adequately cover it on a FR thread. There are those who find a way to claim you get one spouse for your entire life, regardless if you are widowed or not. One and done. They manage to justify this using Scripture. In fact, in seminary, we spent too much time examining all the views in Scripture and in the original languages.
Once you get involved in real lives, it gets messy fast. If I had more time, over coffee, I'd tell you a story from my Mission's professor, whose first assignment was to a church in Haiti... but alas.
Best
Begging your pardon, but your training regarding the issue does not serve you well. Jesus is only speaking of the violation and termination of the pre-consummation espousal portion of the Jewish marriage process. See Deuteronomy 22:13-21 and Matthew 1:18-19.
I'm certainly not wanting to offend you.