To moonlight as a dentist, you would need a full NY dental license, not the limited permit.
Those who go into ortho straight from dental school and don't have a full NY license sometimes get licensed in NJ or CT and moonlight there.
You can see if your credentials allow you to get a full license as a dental hygienist in NY or the surrounding states. Hygienists are in short supply everywhere so it should be easy to get some temp work on the weekends.
