When talking about chores at home I said this to my wife
I hate doing the dishes, though I do them every day, because I love the family.
I'm pretty sure the part before "because" is idiomatic, as it comes from another ELL post.
I'm also sure the part after "because" sounds natural as well, as Ngram Viewer justifies it.
The question is that Ngram Viewer returns "Ngrams not found" for the clause "because I love the family", which implies it's not as common. Why is that?
I think the idiomatic phrase you might be looking for is "because I love my family".
But since the clause beginning with "though" is dependent, and unnecessary grammatically, the "because" clause is taken to refer to the "I hate" clause, which is probably not what you mean (i.e., you probably don't mean "I hate doing the dishes because I love the/my family").
So the real sentence should probably be "I do the dishes every day, though I hate it, because I love my family." You can see that you can leave out the dependent clause in the middle and retain the main meaning of the rest of the sentence.
If you mean that you are doing this because you like the principal of a family in general, as opposed to yours, then you might work "the family" in somehow. "I do the dishes every day, even though I hate it, because I love the idea of everyone pitching in on the family chores."
