The Church would advise that the spouses separate in some circumstances. Typically, spousal abuse and adultery are grounds for separation, unless the wrongdoer obtains forgiveness from the spouse and eradicates the problem.
Once separated, the spouses may seek legal protection for themselves, their children and their property, i.e. obtain legal divorce under the laws that the state may have.
However, neither of that dissolves the marriage. In the eye of God the separated spouses (whether legally divorced or not) remain married. Neither of them may re-marry. That is regardless of the allocation of guilt for the separation.
The only thing that may allow a former spouse to re-marry is if the marriage is declared null. But grounds for annulment are not the same as grounds for divorce. Annulment is possible if (1) it is sought and (2) a defect can be pointed out in the initiation of the marriage. Defects of spousal life after the marriage was properly initiated are not grounds for annulment. For example, if the marriage was not initiated freely (a spouse was coerced) or fraudulent (a spouse was already married and have no right to marry) or not intended as a traditional life-long monogamous union of a man and a woman open to parenthood, then these might be initial defects and ground for annulment.
So adultery may play a role in the annulment process insofar as it points to the lack of intent to form a union of mutual fidelity. Other frequently occurring defects these days that may lead to annulment are lack of intent to have children or openness to a divorce and a second marriage after a while. However, in itself adultery is not grounds for annulment, and without annulment neither spouse is free to marry.
Note also that annulment does not impute that the union was sinful while it lasted, nor confer illegitimacy on the children so long as the spouses assumed, albeit incorrectly, that their marriage was real.
Thanks for the answer.
So it seems that if your spouse commits adultery against you, that the only choice you have if you want to be happily married for the rest of your life, is to have them killed. (which of course would end the marriage) :)
(I realize that reconciliation is the ideal, but I also know that in the bible God gives us permission to divorce in cases of adultery (one spuse already ended the marriage). Sometimes the trust required for marriage cannot be rebuilt.)