He also said they failed to declare major conflicts.
He added that such an "inept and fundamentally immoral cabal" didn't have the competence or confidence of citizens to develop a credible 10-year plan and called on them to resign.
After his submission, Mr Chesterman challenged Mr Law on his criticism of councillors and his "defamatory" comments.
Mr Law said last night he was not in a position to comment over the legal action, regarding which the Herald understands he has been given until July 5 to respond.
Mr Chesterman also declined to comment.
"There's a legal process that's being followed and from the advice of my lawyers I'm allowing that process to occur."
Hamilton mayor Julie Hardaker said it was inappropriate for her to comment, as it was a matter for the two people involved.