Is it permissible for the wife to refuse the return of the first wife to her husband, knowing that the husband wants to take her back for the sake of their children, and is it better for her to ask for a divorce in this case?

It is advisable to be deliberate and not rush, performing Istikhara (prayer for guidance) and seeking counsel. It is not recommended to request a divorce, as it is the most detested permissible act to Allah, and the issue at hand is an ordinary matter that Allah has permitted. The questioner is advised to remain with her husband and be patient. If he insults her or falls short in fulfilling her rights, then she has the right to act. Objecting to the first wife's return is not her right.