Must I sever my ties with my close friend whom I love for the sake of Allah, for fear of being disobedient to my parents, especially given that my parents ordered me to sever ties with another friend, not her?

The rights of parents are great, and obedience to them is obligatory in what is good and permissible. If your father forbids you from getting to know someone online, the basic principle is that you must obey him, because he is preventing you out of concern for your well-being and fear of corruption befalling you. Therefore, sever your relationship with the girl whom your father ordered you to cut ties with, and apologize to her explaining this reason. As for the first girl, whom he did not order you to boycott, she is not included in this matter.