I don't completely understand your concept. What I had envisioned looks like the attached image. The linear actuator will keep pulling/pushing for as long as a current is applied. The direction of the actuator (push/pull) is changed by swapping the voltage polarity which is usually done with a double pole double throw switch.
Once you know the weight of the door, you can select a linear actuator based on load capacity and stroke length to match to your mounting point and the weight of the door (lever arm, moment).