No it really doesn't boil down to "what's for the greater good" as you put it. It boils down to two adults (or at the very least one of the adults...perhaps the healthier of the two) making a choice to deal with destructive behavior WITHOUT involving their children.
Putting your kids through this is doing them NO favors. Instead you are giving them their own BAG full of FOO issues that they will have to deal with later down the road. Sure, we will all have some FOO issues we will have to deal with, undoubtedly....but you two are giving them some DOOZIES. You are potentially setting your own children up to never do well in a committed relationship.
Do you really want one of your kids looking you straight in the eye one day while saying to you...."I'm never getting married, look what happened with you and mom!" Or yelling and screaming in front of their own kids.....because Mom and Dad did it? THAT IS WHAT HAPPENS. It's flat-out reality man!
It honestly sounds to my ears that you have this attitude that "well they can deal with all of this later." because you say "it just happens" that they get drug in....or you all have bigger issues to deal with. This issue CAN be dealt with at the same time. What's to stop you from telling your W right then and there "No! We aren't involving the kids!" and then asking them to leave the room?! That makes you the kids champion and removes them from the scene so that you can deal with the issues? Therefore you are preventing the damage to begin with as best you can and minimalizing the damage they will have to deal with later on in their own lives.
One thing I never had to live with was my parents screaming at each other, thank GOD for that! My parents NEVER discussed divorce in front of me (and they went through tough times too) so I simply cannot fathom what it must feel like to watch your parents go at it, much less....be drug into it.
