Many Church members past and present have had opinions on what will happen in the afterlife in regards to polygamy, but we simply do not know. Not even our leaders know (or if they do, they are keeping it a secret). It is true that a man can be sealed to more than one woman, and it is also true that a woman can be sealed to more than one man. The latter is less common, but it has been known to occur, both when doing temple work for deceased women, and for women whose husbands have passed away while they were still young. How it will be sorted out is not known.

The following is a quote taken from an interview with Dallin H Oaks

HW: There still is some confusion that polygamy is definitively and unequivocally disallowed in this world. What will happen in the next? There is a perception that polygamy is part of the afterlife. Could you talk a little about that?
DHO: If I talked about that I’d be making doctrinal statements where the prophet has not chosen to make doctrinal statements, so I think I shouldn’t say anything except to affirm that a lot of people, myself included, are in multiple-marriage situations. Look at the significance of that. There are a lot of people that live on this earth that have been married to more than one person. Sometimes those marriages have ended with death; sometimes they’ve ended with divorce. What does the next life mean to them in relation to a covenant they once made and so on? I don’t think those people have much of an answer for that question. It might not bother them because they don’t believe that people will live as married couples in the next life. And if they don’t make and live for the covenants to do that, [as for themselves] they’re right! But for people who live in the belief, as I do, that marriage relations can be for eternity, then you must say, “What will life be in the next life, when you’re married to more than one wife for eternity?” I have to say I don’t know. But I know that I’ve made those covenants, and I believe if I am true to the covenants that the blessing that’s anticipated here will be realized in the next life. How? Why, I don’t know.

My opinion is that no one will be forced into a marriage that they are uncomfortable with. Today we chose whom we marry, and I feel it is no different in the after life. I also don’t feel that anyone can take on additional spouses without their current spouse’s permission. But again, this is my opinion.

I am not aware of the Church ever canceling out a child-parent seal. So, yes, the mother’s seal with her children will remain in place after the divorce, as would the father’s.

I think the Church prefers to leave the seal in place between divorced partners until the ex-wife is considering going through with a subsequent temple marriage.

There are three aspects of the marriage covenant that should be considered. 1) the promise between spouses to stay together and the blessing conditioned on mutual faithfulness to that promise (the ability to stay together thoughout eternity). 2) The husband takes on an implied responsibility to economically provide for any children, something he remains accountable for even if aspect 1 collapses through civil divorce. 3) an individual’s covenant with God has promised blessings of eternal life and exaltation (conditioned solely on individual faithfulness) which is intact regardless of the status of one’s marital or former marital partner.

Note that Mormon vocabulary often treats temple marriage and temple sealing as interchangable, when historically that has not been the case. A civil divorce puts closure on aspect 1, no marriage exists anymore, and going forward towards one’s exaltation does not depend in any shape or form with ever getting back together as a marital couple. But I would suggest that the other aspects of the seal needs to remain intact, at least until new seal can renew and reformulate those covenants.

As per aspect 3, moving on towards exaltation after a divorce means repenting of any sins (including any that might have contributed to the divorce) and speculatively (since descriptions of exaltation usually depict a marital state) enter into a more sucessful marriage at some point (lack of adequate opportunity in this lifetime, presumably will not hold someone back in post-mortality if individual faithfulness is sufficient.)

When an ex-wife wants to enter into a new temple marriage and receive a new sealing, she can apply for a sealing cancellation. When an ex-husband wants to enter into a new temple marriage and receive a new sealing, he can apply for a sealing clearance. Either of these has to go through one’s bishop and stake presidency and approved by the First Presidency before a new temple marriage is allowed.

I think aspect 2 may be the real reason why what happens to the original seal in case of remarriage, is slightly different for an ex-husband than it is for an ex-wife. While these things may have have developed from our polygynous heritage, current posthumous sealing practices render such considerations (such as former speculation that there will be polygyny in heaven but no polyandry) irrelevant in my opinion.

Basically either process is like the steps taken in the temple worthiness interview except there is now added accountability and seriousness. The Church does not want to be a party who violate the spirit of the Law of Chastity through serial monogamy. They have historically always been concerned with not enabling “deadbeat dads.” There may be some hesitancy with endorsing a new marriage if there are unresolved sins (like adultery, abuse, addictions) that caused the original divorce and would likely have the same effect on the new marriage. I think that the appeals process aids the level of discernment ecclessiastical leaders can exercise. By (sometimes) consulting the ex-spouse, sometimes these problems come to light, that wouldn’t otherwise.

I hope some of that insight helps or people with more experience than I on this issue will chime in.