Is it permissible for me to keep the two old phones, especially the one that became ritually impure (najis), if my mother asks for them back, out of fear that they might be used in haram (unlawful acts) or that my younger sister might play the Qur'an on the ritually impure phone, potentially using it in disobedience?

You must abandon obsessive thoughts (waswas (definition)). The phone can be purified by wiping it if washing it would damage it. Your mother is permitted to retract her gift and reclaim the two phones, and you must return them to her if she requests them and you no longer need them. As for what you will give your sister, she has the choice, and you should gently advise her against religious transgressions. The phone you believe to be impure is, in fact, pure, and it is permissible to use it.