As "fy" (my) causes a mutation, I'll give the word first, then give it with "my":
my mother - mam - fy mam
my father - tad - fy nhad
my sister - chwaer - fy chwaer
my brother - brawd - fy mrawd
my grandmother - mamgu/nain - fy mamgu/fy nain
my grandfather - tadcu/taid - fy nhadcu/fy nhaid
my aunt - modryb - fy modryb
my uncle - ewythr - fy ewythr
my son - mab - fy mab
my daughter - merch - fy merch
my nephew - nai - fy nai
my niece - nith fy nith
my cousin (male) - cefnder - fy nghefnder
my cousin (female) - cefnither - fy nghefnither
my great-grandfather - hen dadcu/hen daid - fy hen dadcu/fy hen daid
my great-grandmother - hen famgu/hen nain - fy hen famgu/fy hen nain
my grandson - ŵyr - fy ŵyr
my granddaughter - wyres - fy wyres
my great grandson - gorwyr - fy ngorwyr
my mother-in-law - mam-yng-nghyfraith - fy mam-yng-nghyfraith
my father-in-law - tad-yng-nghyfraith - fy nhad-yng-nghyfraith
my son-in-law - mab-yng-nghyfraith - fy mab-yng-nghyfraith
my daughter-in-law - merch-yng-nghyfraith - fy merch-yng-nghyfraith
With the in-laws, these are relatively new words. Formerly the word for "father-in-law", for example, was "chwegrwn" and "mother-in-law" was "chwegr" (probably amongst many

). These are now archaic and not many people would know them these days.
All the above are Welsh words. I think that your point is proven by the fact that there is not really a word for "great-grandfather/mother", but the word "hen" (old) is placed in front in the same way as "great" is placed in English.
There are also words for "uncle" and "aunty" which are widely used and are borrow words from English:
uncle - wncwl
aunty - anti
