TL;DR: The status of the children has no bearing on whether two people can marry, as far as I can tell (except if local laws would ban that marriage)
I checked the general handbook, and as far as I can tell, these are the guidelines that apply:
For sealings (which can be seen as a religious marriage, but isn't quite that), since a couple has to be married in order to be sealed, the same restrictions apply, in addition to all conditions required to be able to enter the temple, none of which apply here. The status of the children appears nowhere.
When two parents are sealed and then have children, those are automatically part of that covenant and receive the associated blessings. When a couple gets sealed that already has children, those children can be sealed to their now wedded parents to be a part of that eternal family. The only restriction for adult children is that they too need to be endowed (so have made temple covenants of their own). I don't see anything related to the children's wedding status.
The church does condemn incest, and the now-step-siblings would be included in that, but I have strong doubts this situation as described would by reasonable local leaders be seen as such. Again, local laws apply.
Since a comment asked whether this situation messes up family tree records: Only if you maintain them wrong. The records need to able to record any messy situations, including plural marriages, unknown fathers, adoptions, and so on. FamilySearch, which is used a lot by members to do their family history and is the source of information for the proxy temple ordinances, can easily record multiple parent pairs, for example. We perform our proxy ordinances (sealings are most relevant here) for all these pairs, and let God sort out our mistakes in the afterlife.
For example, in life a woman is to be sealed to only one husband, but in proxy ordinances we would seal her to all her husbands and let God and the dead decide and fix what is right.