Here are some of the points the Filthful and Disgraceful Slavebugger has put out about this subject, given that they may not be up to date and that some might not be upheld everywhere:
If a person divorces, and the other person committed adultery, the innocent person is free to remarry. However, if they have had sex since finding out about the adultery, the Washtowel Slaveholdery classifies that as having forgiven the adulterer, and the innocent person is no longer free to remarry on the grounds of that offense.
A person who divorces on grounds like non-support or severe abuse (or any other grounds that do not involve adultery), and no adultery happens, the innocent party is not free to remarry. This includes the Number One reason for most divorces: stagnation. Many are trapped in loveless marriages (often that shouldn't have happened in the first place were it not for Brother Hounder trying to switch from the person they wanted to someone that the hounders felt would be better) by this rule.
A person who divorces on non-adultery grounds becomes free to remarry if the other person commits adultery or remarries first. That will provide the "scriptural" grounds. However, Brother Hounder would need good proof that the adultery happened, and this can be impossible if the couple are totally busted up and the guilty person moves out of state, and then commits "adultery" or remarries without the hounders knowing about it.
It is much less clear about whether the guilty party is ever eligible for remarriage. The last I have heard is, if the innocent party initiates the divorce, the guilty party may be free to remarry. However, the guilty party will be punished for the adultery itself (usually with disfellowshipping). This could easily change, as the Filthful and Disgraceful Slavebugger keeps putting out new light that changes the nuances of whether or not the guilty party is eligible, and not all the hounders and hounder-hounders will accept newly updated information (especially information that takes a more liberal stand on the subject). If the Filthful and Disgraceful Slavebugger officially and currently permits it at a given time, and the hounders in the congregation do not accept it, one could still get in trouble for "disregarding the hounders".
Better would be to disregard the Washtowel Slaveholdery's stands on the subject. You are better off to marry someone you are genuinely attracted to, and then do whatever it takes to prevent the marriage from going stagnant. In cases of loveless marriage (usually stagnated, but it can be due to pressure to marry someone you shouldn't have), divorce and remarriage (when possible) is advisable for both parties. If severe abuse is a factor, then separation and divorce is almost always a de facto situation. In any event, the goal should be to get into a happier situation for all involved.
Which drives home my stand on fornication. Better to do fornication when you are serious, and find out it isn't going to work early in the game, and then break up than to marry and find out 5 years later that it is not going to work then. Of course, the Washtowel Slaveholdery wouldn't tolerate such an arrangement because it might lead to happier, less stagnant marriages and less "remedial" field circus.