I have one question. Object that is controled by player has a collider that is trigger and when it collides with other object i want them to become "a part of him", like they are glued together, and to go wherever he is going.
In case the object had any other movement code, you might want to disable it. For example remove any rigidbodies (or possibly make them kinematic but I don't know by heart if it carries over well to parented objects).