The first of these words means "to control, govern, regulate, or tower above": "The superintendent dominated the hospital staff." "The tall pine dominated the coastline." Domineer means "to rule or govern arrogantly and tyrannically," "to regulate like a despot": "Mussolini domineered (or domineered over) his countrymen for some twenty years." Domineer has more unpleasant and unfavorable connotations than dominate, but neither suggests a happy situation for those being regulated.
Dictionary of problem words and expressions. Harry Shaw. 1975.