I don't mean to be harsh, but don't you think you kinda brought this second mess on yourself? You actively chose to get back a tradesperson who you already know made a potentially life-threatening mistake and he wasn't even able to fix it when told about it originally! What made you think his second-fix plumbing in your bathroom would be any better?
If he didn't provide a quote, what did he agree to? What do you have in writing? Did you take detailed photographic evidence of his mistakes before you fixed them? If you've got pics, ask him for an itemised bill, and then you can prove that he didn't actually fulfill those things properly and therefore you're not paying.
But to be brutally honest, I think you partially brought this on yourself and might need to chalk it up as not-too-expensive life lesson.