Is a father entitled to refuse to marry off his daughter to the one she loves due to old disputes with his family? And is what happened a result of seeking guidance from Allah (istikharah), or is it fate?

If your maternal cousin's son is a man of religion and good character, then you should not refuse to marry him merely because of a past disagreement, for religion encourages marrying those whose religiosity and character you are pleased with. If the marriage did not materialize after performing Istikhara, then that might be a result of it. Do not grieve over what has passed, and say: "This is Allah's decree, and He does what He wills." It is not permissible to communicate with a non-mahram (definition) young man, as this closes the door to fitna, and it might spoil his engagement. Marriage is a provision [from Allah], so entrust your affairs to Allah, and ask Him for a righteous husband, while also taking the necessary steps to search for one through trustworthy individuals. Do not blame your parents for what happened; for that is harming them and is an act of disobedience.