I am aware that sealings between spouses can be canceled under certain circumstances. Can sealings between parents and their children be canceled under certain circumstances (such as child abuse) as well?
Abuse is a very serious matter that can be addressed in better ways than through the internet. But your primary question about cancelling sealings between parents and children are a high level doctrinal matter that you may have misunderstood.
Sealing to one another in any form is not a pair of “divine handcuffs”. It is a method of us as fallible mortal beings becoming one.
Behold, this I have given unto you as a parable, and it is even as I am. I say unto you, be one; and if ye are not one ye are not mine. D&C 38:27
Why would the Lord want a big mass of flawed human beings to become one? We’re just a ball of sin and discontent. What good is that? It isn’t. We cannot offer our impure souls as an offering unto the Lord.
What we CAN do instead, is to offer up our broken hearts and our contrite spirits as an offering unto the Lord. We can all admit our sin, our weakness, and all our flaws as unworthy of Him. We, every one of us, truly are unworthy of the Atonement of Christ. But that is precisely why the Atonement was necessary in the first place.
Being sealed creates a connection (a welding link) between all members of the whole human family like a web or net. That divine spark within each of us is the node where each link connects. As we come to Christ in our weakness and partake of his atonement, the sin and weakness is broken off to form the empty spaces that are found in nets. All that remains is the divine spark (nodes) and the welding links (sealings). For His own reasons, Our Father has determined that family links are the method in which we are to perform these ordinances.
To further address your question, you’re probably interested in what happens to children if a parent does not live up to divine covenants. Or conversely, what if a wayward child fails to live up to his or her covenants either. Do the grandchildren lose all hope of being part of the welded chain back to Adam?
I don’t know any primary sources which address these questions. But I’ll give my personal opinion based on many discussions with people who may or may not know (sorry, that’s the best I can do here). That is that if a parent fails, then the children are automatically raised to replace them, and are directly linked to their earthly grandparents.
I say this is my best guess because it is really the only thing that seems to make sense to me. Families are much more important to our Heavenly Father than they seem to be to us mere mortals who have spent decades now in a society that welcomes unwed parents, adoptions to gay couples, and multiple generations of broken homes. Keep in mind that none of these things are the way families are supposed to function. This is not the Lord’s way.
I’m sorry I can’t directly answer your question because there really is no answer. But I hope I gave you a better understanding of what is really happening with a sealing.