It definitely helps convey the emotion of those scenes you've added it to Master Qui-Gon, though I'd argue that the Titantic theme as the soundtrack to a dog taking a dump in the park would make for a sad scene
Surely there's a piece of Star Wars music or a John Williams track from another film that will help still drive home that emotion without having to resort to Titantic? Alot of ROTS has some emotive music. Even "Across the Stars" has a certain sadness to it and might make better sense considering Anakin's motivations for turning in the first place.
Maybe try that? Otherwise, LOVE the work you're doing (especially the Jedi Council scene in TPM, excellent!)