Is it permissible to supplicate for the facilitated return of the children's mother to bear the responsibility of raising them, while the husband rejects this?

There is no harm in supplicating for the betterment of the relationship between spouses and for the reunification of their family. One must be gentle and kind to the husband's children, as this is among the greatest acts of proximity to Allah, based on the Almighty's saying: "And do good; indeed, Allah loves the doers of good," and the Prophet's (peace be upon him) saying: "The most beloved of people to Allah are those most beneficial to people." The husband is not permitted to leave his wife's matter pending; rather, he must either retain her honorably or release her kindly. The husband does not have the right to threaten you with ending the marriage if anything happens to his children, and you are not obligated by Sharia to accept their residency or care for them except with your consent. It is more appropriate for the husband to strive to mend what is between him and his wife, as custody is a right for both parents as long as the marital bond exists. And the guardianship of discipline has its Sharia-based regulations.