Sounds as though spring pressure is causing the trigger to be canted which means the trigger pin is hitting the frame and missing the frame opening on the other side.
You may have to pull the trigger pin out a bit, and start a second pin (of a similar size/diameter) from the other side, using the pin already in the gun to help position the trigger so that the trigger is level and the trigger aligns with the opening on the other side.
Push the second pin in. if things get aligned properly, you'll be able to put the trigger pin on in and drive OUT the second pin, because it will be aligned with the opening on the other side of the frame.
(I'm suggesting this based on your description....there may be something else out of position and I've misdiagnosed.)
Finding a pin of the proper diameter that can be inserted from the other side may be a problem. Some nails may be close to the right diameter, as will some small screwdrivers or punches. If using a nail as a pilot pin, you'll want the point to be flat.
A local gunsmith should be able to handle this quickly, unless something really got screwed up inside the frame, if you're aren't able to get things back right.
