Is it permissible to marry a girl who was engaged for five years, and then doubt arose that she might be a suckling sister, with conflicting statements and differing fatwas?

You mentioned that your mother, may Allah have mercy on her, told a family member that she breastfed one of your maternal uncle's daughters. From the context, it is understood that one of them is your fiancée. It appears that this breastfeeding was not legally established and cannot be considered valid, because this statement was not proven to have come from your mother, and it was only relayed by one family member. Even if we assume she said it, she did not specify which of the daughters she breastfed. And even if we assume she specified your fiancée, that does not prove anything, and it is recommended to avoid it. So, if you avoid it, that is out of piety and precaution. But if you prefer to marry her, that is permissible for you.