It almost sounds like it was written, both music and lyrics, by the OP. Then someone re-orchestrated it, that is, keeping the same exact notes and lines, but different instruments. Then it was re-arranged in a new setting, but was still the same piece. I think...
In that case, you'd be the composer and lyricist (though you could just put "By" and your name). The person who re-orchestrated it the first time doesn't matter unless you use that orchestration, in which case it be "By" you and "Orchestrations" by him/her.
If you are using the re-arrangement, that is, the final product with all the extra stuff such as expanded intros, that would be "By" you and "Arranged" by him/her.
The two products are actually different. If your name was "A", the first person who changed the instruments around was "B", and the person who rewrote the song to have a better feel to it was "C", it'd look like this:
The version which you wrote but the person changed the instruments: By "A", with Orchestrations by "B".
The version which was changed to have a better feel: By "A", Arranged by "C".
I agree; that was hard to determine what you were asking. If the two finished products were based on your original song that only you wrote the music and lyrics to, then you are the composer. Changing instruments around or adding new material to stretch out someone's else's work does not count as being a co-composer.