All this talk about Billy obsession with Chancellor, one could argue the same about Lily's obession too.
I mean she faked a whole kidnapping and used her own kids to win back Chancellor. She just wasnt doing all that because she was mad at Cane and wanted teach him lesson, she saw an opportunity and went for it, so I actually see nothing wrong with Billy going after what is rightfully his family, its not like Chancellor was left to The Winters or anything.