Is the marriage contract that took place under duress and threat valid, and is it permissible for me to kill my daughter for committing this act, and how do I deal with this problem given our rejection of this marriage?

The young man's threat of suicide does not constitute compelling duress, and therefore, the marriage contract is legitimate, and your daughter has become his wife. It is advisable to complete the marriage if the young man is suitable and your daughter has developed an attachment to him, as the Prophet, peace and blessings be upon him, said: "Nothing like marriage is seen for those who love each other." This is better than the continuation of a forbidden relationship. As for killing her, it is not permissible, for it entails loss in this world and the hereafter. Allah, the Almighty, said: "And whoever kills a believer intentionally, his recompense is Hell, wherein he will abide eternally, and Allah has become angry with him and has cursed him and has prepared for him a great punishment." Also, the Prophet, peace and blessings be upon him, said: "A believer remains within the scope of his religion as long as he does not shed unlawful blood." It is recommended to treat her kindly and guide her towards good.