I’m not a solicitor, and hopefully one of the solicitors who subscribe to this site will correct any mistakes but, if all you are trying to do is find some obscure law that you think will help you force your solicitor to keep representing you – there doesn’t seem to be one.
As earlier – a solicitor has the right to apply to the court to withdraw from any case at any time. To do this, they have to file a motion. As I understand it, a motion is a procedural request to the supervising judge. You will be served (I think) a copy of the motion and the affidavit and will probably (?) have a chance to respond after which the judge will decide whether or not the solicitor must continue to represent you.
Order 52 of the Rules of the Superior Court
MOTIONS AND OTHER APPLICATIONS
1. All interlocutory applications to the Court and all applications authorised by these Rules to be made to the Court shall be made by motion, save as otherwise provided by these Rules.
I feel sorry for your solicitor as you certainly come across as an awkward person to deal with. Believe it or not, professional people like solicitors, doctors, teachers, etc. have rights too, and that includes the right to say, no I don’t want to work with you and I am therefore going to employ the neccessary procedures to terminate our professional relationship.