Please forgive me a bit for mixing different ideas over multiple post in this thread with a bit of overlap. I consider the ability of a language to specify relationships very valuable and underdeveloped in English. Latin has a word for mother of father. English has only grandfather or grandmother. It has ugly constructions like great-grandfather.

In my draft I have the following root words:
ba = 0
ce = 1
di = 2
ma* = female
ne* = male
caiq = parent

Out of those roots I can create: caiqma = mother
caiqne = father
caiqce = grandparent
caiqcemaba = grandparent (parent of the mother)
caiqceneba = grandparent (parent of the father)
caiqcemace = grandmother
caiqcenece = grandfather
caiqcemana = grandfather (father of the mother)
caiqdi = great-grandparent

This way of specifying relationships is quite efficient. In case you want to distinguish your parents not by gender but by which parent is older and which is younger, you can simply use the syllable for "younger" instead of the on for "female". That way the language can translate easily from languages that have different words for older and younger brothers, while not forcing lanugage users that don't want to make distictions based on gender or age.

Why four letters for caiq? Because it's based on cai with simply points to the parent node in any graph. Combing cai with the sylable for knowledge from authorities fwe, caifwe becomes teacher. It's easily extensible so that caifwece is the teacher of my teacher. English has no word for teacher of my teacher and my language can still do it in 8 letters. It can even do teacher of the teacher of my teacher in 8 letters a case where English feels like Pirahã.

Do other words for family relationships are:
fuiq = sibling
caiqfuiq = aunt/uncle (parent's sibling)

Out of that a person with the same teacher as me (classmate) becomes from the structure we already have fuifwe. We get a new word of caifuifwe with means a person with whom your teacher learned together under his teacher. We get that word without the language learner having to learn it explicetly.

There will be many cases where more complex relationships can be easily expressed with that system. Via Sapir-Whorf I would expect that this well structured system of relationships makes it easier to think about more complex relationships.

*ma/ne : Those are very provisional. Likely it's no good idea to have two nasal consonants at this place but instead use two consonants that differ more from each other to reduce the cognitive effort that's required to hear whether someone says one or the other.