I think OP's second version is a failed attempt at a cleft sentence. Simplifying, we have the non-idiomatic form...
1: This is a sentence which its language is English. (its = possessive this sentence's, not it is)
...which is trying to fuse the two separate clauses / sentences...
2: This is a sentence. Its language is English.
The idiomatically correct way to join those two is...
3: This is a sentence whose language is English
Simplifying even more, we can remove the "possessive" element and consider...
4: This is a sentence which it is written in English. (NON-IDIOMATIC, as per OP's example #2)
...which non-idiomatically attempts to fuse...
5: This is a sentence. It is written in English.
The idiomatically correct versions are...
6a: This is a sentence which is written in English
6b: This is a sentence that is written in English
6c: This is a sentence written in English (the "relativising" element can validly be omitted entirely)
6d: This is a sentence. It is written in English
Note that whereas we can completely discard the "relativizing" element in #6c above, we can't do this with the possessive forms (the family's house, the sentence's language).
I don't think there's a clear-cut grammatical justification for rejecting the syntax of my examples #1 and #4, which looks to me very similar to the subject of this ELU question. Essentially, what we have is "redundant relativizers" (the contextually-relevant family / sentence has already been referenced by the pronoun it, so there's no need to reference it again using which, that, or possessive whose). It's just not idiomatic (today, at least, but I suspect such constructions might have been more acceptable a couple of centuries ago).
Thanks to @snailcar for suggesting that the constructions we're dealing with here involve (failed) attempts to use resumptive pronouns. I'm not 100% sure, but I suspect the reason they fail is because they violate Ross Constraints (as covered in that link by our very own John Lawler).