In some Earth cultures, it is important to distinguish the genders of people. If this is something you feel is necessary in your version of the Mandalorian culture, there is one option to do this in Mando'a. This quote from KT to show us how the author envisioned the gendered adjectives being used: "Ke ba'jurir gar'ade, jagyc'ade kot'la a dalyc'ade kotla'shya."
Following this, you simply put the appropriate gender adjective in front of the relationship that requires such identification. For example, use dalyc'buir for "female parent" and jagyc'buir for "male parent." Per the author's suggestion that betene (apostrophes) are optional, dalyc buir and jagyc buir are also correct. Alternatively, use buir as a suffix attached to the person's first name, to speak about or to a specific parent.
However, do not feel that you must adhere to the traditions of any Earth culture. Remember that Mandalorians are part of a different culture than most of the ones on Earth, and thus have their own ideas of what is "right" and "wrong," just like each of the cultures and families that we each grew up in have their own rules. For example, some fan discussion ponders what exactly "daughter" and "son" mean in the above statement in a culture that supposedly severely downplays gender roles. My personal preference? That the words have to do with broad personality types, like dalyc might "introspective," while jagyc could be "extroverted."
In the case of what to call parents or other relationships, because gender is of little importance to them, we fans presume that Mandalorians come up with different terms. Maybe it's the first name; maybe it's some baby-version of the name; maybe it's something else (such as we see some of the clones call their adoptive father "Kal'buir").
The differences are just part of the culture, even if they seem very strange from the ones we grew up with, just like every culture on Earth has customs that appear strange to those outside it.