Barn - singular indefinite Barnet - singular definite Barn - plural indefinite Barna - plural definite
If you use the first concept (noun in definite + possessive), it is going to be barna dine, if you go with the other structure (possessive + noun in indefinite), you will end up with dine barn.
But what is the difference?
I understand definite forms such as barna as similar to "the children" whereas indefinite forms such as "epler" as askin to "(any) apples".
In the phrase "Barna dine", I can read it as "(The/These/Those) children (of) theirs"; whereas in this case, since barna is indefinite, the sentence reads like "(any) Children of mine".
What are the differences in Norsk? When would one use the definite form and not the other?
You are correct. Barna dine = your children. Barnene dine is the same thing. I believe in one of the desktop lessons Duo teaches that neuter nouns, when definite plural can be suffixed with -a or -ene, but most often people use -a with barn just because of convention but barnene is also grammatical.
When you put the posssssion after, it must be in definite form:
Dine barn - good Barna dine - good Dine barna - bad Barn dine - bad
Even though "barn" can mean plural, it has to be definite if the possession comes after.
This is my basic understanding. Anyone please correct me if I have something wrong
When talking about possession of things in Norwegian, placing the possessive first generally put an emphasis on the ownership. However, that is not the case when we talk about people, like in the above example, as we don't own people like we do things.
As for the "indefiniteness", you can find something similar with possessives in English:
"That is my child." (not explicitly definite)
"That is the child of mine." (definite)
The expressed definiteness or lack thereof the noun doesn't change the meaning, as the possessive already implies that we're talking about a definite someone or something.
In Norwegian, it's the position of the possessive that creates the nuance in meaning. The noun's grammatical definiteness is just another consequence of the possessive's placement, as we're talking about a definite something or someone regardless. I hope that helps. :)