how do I go about filing a motion with the court to have a lawyer removed off a case because of conflict of interests issues?

In small claims court, any matter can be addressed to the judge.  I believe that is what municipal court is in NJ, although I am not licensed there. In PA, you would attend the hearing and raise that issue as a threshold matter.  If the judge agrees with you, he should relist the matter to give your opponent time to get another lawyer.  But a conflict only arises if the other lawyer either represents you now in the same matter, or represented you in something else which gave him knowledge that could be used against you.