Linda,
From what you describe, the furnace is doing it's think correctly. Sounds like it is getting starved for Propane when running on the right tank.
Couple of things to consider on the right side tank:
The tank safety valves sometimes stick, and your's may not be fully open. I believe a refill station can reset it all the way for you, or
There may be moisture or oil in the line from the right tank to the regulator on the left. Might help to try and blow it out (be sure to remove the line from the regulators or you will damage the regulators, or
Last, but probably the most likely - the little red regulator on the right side is failing - which is pretty common. It is relatively cheap and might be worth a try just to replace it.
Good luck, and Welcome to the Forum!