If Rem thought light was such a disgusting person, why didn't she kill Light first. From there, she could convince Misa to stop killing and some how avoid being caught oder Kill L as a last resort?

The creator of the manga, didn't really approve of LightxMisa like the ones that did the anime. Though. He didn't care if people wanted them to be. Here's the thing. Light has been giving pointers that he had interest in L. And only him. It was obvious that Death Note was meant to be a yaoi. But he loved Misa. They kept her to prevent people from thinking he's gay. When that's false. In the manga, he copies Kiyomi in the Manga 13 panels. He was meant to stay with Kiyomi. Because in one of the chapters. I think it's where Mikami is in the cover. Uhm. His reaction shows interest in her. He had never shown interest in Misa. But the creators adored Misa. And forced her to stay. She wasn't needed after losing her eyes. L only needed a confession. Couldn't Du tell? He kicked her out after it was confirmed that his doubt was in the grey. But he still thought Light to be Kira. It's painfully obvious that Light hated Misa, but they pushed her in. If they hadn't, Misa would've disappear like Kiyomi. Kiyomi was lost. In the Manga 13. She wasn't going to return. Why wasn't Misa? Rem. I pity Light. I only loved that he hated evil. But he ends up manipulating Kiyomi and I Lost interest in him. I no longer felt pity, but a bit of hate. I hate Misa, because she's stubborn. And no. Not just because she's annoying. But because she was a waste of space. She wasn't funny. I Liebe LightxMisa fans, because they are a good laugh. To read their comments. But my life is relaxed, knowing that not of this shit is real. K.

Don't think i can beat the detail on that. Kinda looks like my english exam. Was good, but didn't really answer the question.
I recall Rem sagte in the Anime (not sure about the Manga tbh) that the only reason that he is keeping Light alive is because he makes Misa happy. However he then took a little of a liking to light hence why he died when he killed L.