Is it permissible for me to marry the girl I love despite my parents' objection, due to previous family disputes and a bad reputation of one of her female relatives, and would that be considered disobedience to parents?

Obedience to parents takes precedence over marrying a specific girl, unless the young man fears a negative consequence by not marrying her. In that case, he may marry her even if his parents are not pleased. However, if it is possible to avoid marrying her to prevent problems and show filial piety to the parent, that is better. If marriage to her is not destined, then the relationship with her must be severed, as a relationship between a man and a non-mahram woman is a gateway to corruption. Love can be managed. One must be cautious not to falsely accuse people of immoral acts, especially fornication, unless there is clear proof, lest it lead to the grave sin of slander.