Is it considered an act of disobedience (ʿuqūq) for a friend not to see her mother except a few times over many years, then to communicate with her by phone? And does the parents' separation affect the ruling on a daughter's disobedience to her mother?

Your friend's cutting off her mother and her failure to maintain ties with her and visit her for these long periods, despite her ability to do so, constitutes disobedience ( 'uquq ). Allah has made it obligatory to show kindness to parents, even if they are disbelievers who call to disbelief. No matter how much parents fall short in their duty to their child, their right to kindness does not fall away. Connecting only by phone is not sufficient if a meeting is possible, unless there is a hardship such as a long and costly journey. Kindness to parents is to show beneficence towards them and to do what pleases them, as long as it is not forbidden. Disobedience ('uquq), on the other hand, is anything that causes significant harm to a parent. Maintaining kinship ties is achieved by doing what makes you a maintainer of ties and not a severer of them, such as fulfilling needs, visiting, writing letters, and sending greetings.