How can the problem of a young man, married to a divorced woman who refuses to leave him, be resolved, given her father's refusal of marriage by Fatiha and the difficulty of polygyny?

Marriage without a guardian is not valid. Therefore, if the guardian cannot be persuaded to agree, the forbidden relationship between you must be severed, as it is a cause of fitna and corruption. The girl can be threatened with informing her guardian to deter her from continuing the relationship.