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Please see Title. I'm not specifically referring to which language they came from... but if they come from something else. In other words, do they come from words with other meanings.
For example, do words for children come from a word that means "being that comes from one's loins" or something.
I extracted the following from the online Webster Dictionary. It's interesting to see how all these words were transformed from Latin/Greek/Old High German/Middle English to the current English words.
Note: I know that this does not exactly answer your question, since you actually want to know if the words derived from words with other meanings. But I think that having the full list of originating languages here may be useful as other answers to your question may refer to it.
DAUGHTER
Middle English, doughter, from Old English dohtor; akin to Old High German tohter daughter, Greek thygatēr
First Known Use: before 12th century
SON
Middle English sone, from Old English sunu; akin to Old High German sun son, Greek hyios
First Known Use: before 12th century
AUNT
Middle English, from Old French ante, from Latin amita; akin to Old High German amma mother, nurse, Greek amma nurse
First Known Use: 14th century
UNCLE
Middle English, from Anglo-French, from Latin avunculus mother's brother; akin to Old English ēam uncle, Welsh ewythr, Latin avus grandfather
First Known Use: 14th century
MOTHER
Middle English moder, from Old English mōdor; akin to Old High German muoter mother, Latin mater, Greek mētēr, Sanskrit mātṛ
First Known Use: before 12th century
FATHER
Middle English fader, from Old English fæder; akin to Old High German fater father, Latin pater, Greek patēr
First Known Use: before 12th century
COUSIN
Middle English cosin, from Anglo-French cusin, cosin, from Latin consobrinus, from com- + sobrinus second cousin, from soror sister — more at sister
First Known Use: 13th century
NEPHEW
Middle English nevew, from Anglo-French nevou, neveu, from Latin nepot-, nepos grandson, nephew; akin to Old English nefa grandson, nephew, Sanskrit napāt grandson
First Known Use: 14th century
NIECE
Middle English nece granddaughter, niece, from Anglo-French nece, niece, from Late Latin neptia, from Latin neptis; akin to Latin nepot-, nepos grandson, nephew
First Known Use: 14th century
Reference:
etymonline.com gives the origins and original-language meanings of most of these words (with the exception of the meaning of "daughter", which John Cowan describes in his answer).
In brief, focusing on meanings:
Mother meant "female parent" in Old English, and presumably something similar in its origin languages. It was
"[b]ased ultimately on the baby-talk form *mā- (2); with the kinship term suffix *-ter-"
Father derived similarly, but there is this additional note:
Spelling with -th- (15c.) reflects widespread phonetic shift in Middle English that turned -der to -ther in many words
Son is ultimately
a derived noun from root *seue- (1) "to give birth"
and came to mean "son, descendant" in Old English.
Cousin:
from Latin consobrinus "cousin," originally "mother's sister's son,"
Nephew in PIE meant
"grandchild," and in a general sense, "male descendant other than son"
This became "sister's son, grandson, descendant," in Latin. Niece is a Late Latin feminine form of the Latin for "nephew".
Aunt has this:
from Latin amita "paternal aunt" diminutive of *amma a baby-talk word for "mother"
And uncle:
from Latin avunculus "mother's brother," literally "little grandfather," diminutive of avus "grandfather," from PIE root *awo- "grandfather, adult male relative other than one's father" [...] Replaced Old English eam (usually maternal; paternal uncle was fædera).
Child, similar to the example sentence in the question, relates to words meaning "womb"/"pregnant", coming to mean ""fetus, infant, unborn or newly born person" in Old English.
I was searching for the origin of daughter in my mother language, Persian, and then I found this post and I thought it's worth sharing it. In ancient Persia the young female member of family, basically daughter, were called doog taar 'doog' meant milk and the 'taar' at the end makes it a noun meaning the person who milk the cows. This later changed in Persian to dookh taar and now in Farsi dokh taar - kh in Farsi is pronounce pretty much similar to German's gh and this word in German is pronounced very similar to Farsi.
Just in case someone needs a reference here is the link to Wiki, however, it's in Farsi language: This Link
Mother, father, son, brother, sister have pretty much always meant what they mean today. It's clear that mother and father are ultimately derived from adult reinterpretation of babies' babbling things like /mamama/ and /dadada/; this is a worldwide process that gives us both informal and formal words for parents, and is constantly self-renewing. Brother and sister may also be of this type.
Daughter, however, is ultimately 'milker', from the Proto-Indo-European root *dheugh- 'press, touch, milk'; this change in meaning goes back to before PIE broke up into the various families. All these words except sister have a common suffix, whose meaning is unknown; sister picked up its /t/ at the Proto-Germanic stage, and the other language families do not show /t/.
I have the idea that Latin pater (father) might have been ○parantor (para.tor pa...tor pater), from the verb parare meaning prepare. So the idea might have been: He who was the preparing part.
No idea as to Greek thygater. I have the impression it is a word from neighbouring languages the Greeks have adopted and perhaps transformed.
