Legal Question in Family Law in California

Only if by litigant, you mean the very same petitioner. It would be a very attractive power to get rid of the other party's lawyer, but its not allowed, short of misconduct or an actual conflict of interest on the attorney's part with his own client. Even in that case, the client may opt to waive the conflict and retain his attorney.

If you are trying to remove the other party's lawyer, you can only do so with a motion to disqualify. You would have to show that there is a conflict of interest involving you, and not the other party.