Manipulate means to influence or control someone indirectly, mainly for a personal gain. The word itself has a very negative meaning. 'She manipulated me into going to the party' = I didn't want to go, but she made it so I didn't have a choice to not go. Maneuver on the other hand is a bit more neutral although can be used in a negative context as well. It implies strongly that there was a tactic or plan behind achieving a goal. 'She maneuvered me into going to the party' = She made a plan so I would have to go to the party.