One thing I have found when working some of this type of puzzle - when you get into complex ones, there comes a time when direct interpretation of the clues does not provide the solution. You have to assume something, and then prove your assumption correct or incorrect. If you end up proving your assumption incorrect, then you have to go back and remove all the markings you made based on that (now proven incorrect) assumption. I don't know how to do this kind of "assumption marking" at this online website. When I have done these complex ones in the past, I have printed the puzzle out on paper and used pencil and eraser and some marking strategy I dream up to solve them.
The website appears to let you mark "knowns", and "possibilities", but not "assumptions that need to be proven, and their trickle-down marks". At least I can't find how to do assumptions.