I went the distance she went.
Is this sentence kind of an appositive case? Can we think of "that" as omitted in the sentence as in "I went the distance (that) she went? Here, "that" is leading a clause as well as referring to "the distance". Like this, if "she went" is used appositively, can we grammatically omit "that"? This case seems to have something to do with this case in which "the way (that)" is used because we normally don't include "that" when we use "the way (that)" as in "I like the way (that) you're.
But there seem to be also some people who argue that this "that" is just a relative pronoun. But as for the verb "go", I wouldn't agree with them in that generally most native speakers tend not to regard "went" as used transitively in my sentence and if "the distance" is really the object of "went", this sentence (I went the distance, which she went) must sound correct to all native speakers, but as far as I ask them about it, just only few of them would think of the sentence as grammatically correct.
To sum up,
Is my sentence an appositive case?
If 1 is right, is it grammatically acceptable to omit "that" in the sentence?
If 2 is right, can you answer on when to able to grammatically omit "that" or not?
Does that sentence have something to do with "the way (that)" usage?