Is it permissible to marry a young man after divorcing a cruel husband, knowing that the family will force [her] to marry someone else to defend their honor?

You must sever this forbidden relationship with this young man and repent to Allah. The husband's neglect or harshness does not justify this relationship. The wife must either separate from her husband through divorce or khul', or endure it and preserve his honor. A righteous wife guards her husband in his absence, as Allah Almighty said: "So righteous women are devoutly obedient, guarding in [the husband's] absence what Allah would have them guard." This relationship is a betrayal of trust and an overstepping of Allah's boundaries. Therefore, sincere repentance and abundant acts of obedience are necessary. Try to reconcile with your husband and remember that the foundation of marriage is affection, understanding, and patience with mistakes, and divorce should not be resorted to except when reconciliation is impossible. If the situation does not improve, there is no sin in seeking divorce or khul', and after the 'iddah period ends, it is permissible to marry whoever proposes to you.