Are the young man's parents entitled to refuse his marriage to the girl he desires, especially after their engagement was previously broken off due to family disputes, and is it possible to convince the parents to agree to this marriage?

It is advisable to seek the mediation of wise individuals to reconcile the family, along with prayer. The family's refusal of their son's marriage without legitimate reasons recognized by Sharia is not permissible. If the parents insist on him not marrying, he must comply, unless he fears harm. This is contrary to their command for him to marry someone he does not desire, in which case obedience is not obligatory. Remember the verse: "But perhaps you hate a thing and it is good for you; and perhaps you love a thing and it is bad for you. And Allah knows, while you know not."