Yeah, you're kind of mixing up two separate questions.
1) Do you have the right to? No. Just no. No qualifications there.
2) Will YT take it down? Unlikely, but with the music key contractual changes brewing, it's all likely to be a dead issue soon as they won't take ANY infringement down, but rather automatically monetize it for the artist you took it from. They've been inching toward that with content ID for some time now.
Frankly if a remix can't even fool contentID, it likely wasn't remixed much.