I'm a Stander, we all know that. But when there has been adultery, is there something offical Biblically that needs to happen to return the situation to the vow... because some that take back their spouse may change their mind later--perhaps in their own MLC.
True repentance of the adulterer. That's it.
When their spirit has been convicted and their heart is contrite, it is my belief that it is God's will that the injured spouse forgive and if they can truly accomplish that (with His help), the marriage is wholly restored - as if it never happened (yes, we all know the continued work that is necessary however, the sin is removed, as if it never occured). Should the previously injured party later go on to commit adultery, the damage he/she would then be doing to the marital union is on them (so to speak) and not lessened one bit simply because they could (and probably would) say "Well, YOU did it!".
I would want to renew my vows if my husband and I were to ever actually pull this thing off. That would just be my personal preference, though. There is nothing biblical to support it as a "requirement". For me it would just be one anointed and glorified final swipe of the eraser.
And as an added perk for this flesh of mine, it'd be one huge "HAAAA!!! TOLD YA!!" to the enemy that would quite simply ROCK.