Is the husband considered to have violated the solemn covenant and the condition of the marriage contract if he refuses the unorganized presence of his wife's children from her previous marriage in the home, knowing that he had agreed to their permanent stay, but the children's father refused and demanded random visits, while the wife desires a specific arrangement for visits?

There is no blame upon you for requesting the organization of your wife's children's visiting hours with her. This is not considered a breach of the condition, for homes have their sanctity and privacy. The Sharia has taken this into account by ordaining seeking permission even for children who have not reached puberty. Therefore, your wife, her children, and their father must observe this to avoid causing embarrassment.