Simple terms, the low pressure side of the a/c, the return, does not move air very well. The high pressure side can move air a lot better. Have you changed the filters recently? What kind of filter are you using? Does the bedroom return have a filter or should have a filter? Can you feel air coming out of the supply ducts and air going into the return in the bedroom?
The fact that this was installed makes me think that they were trying to make the bedroom more comfortable.
The reasons are many for improper air balance/preformance. Most fall to the installer. You do not say how old the home is. When was the last time the units were serviced/inspected? Have you checked the evaporator coil in the attic for clogging?
I suggest that you call a pro, and not the company that installed the units. As for a complete check out of the system and changes suggested. Ask for the manual calculation to be done and verify that the manual calculation solution is indeed what you have installed.
I purchaced a newer home by a national builder. Preformance on the a/c sucked from the beginning. I called another contractor and was considering changing the equipment. The first thing that the contrator said was that the plenum on both sides of the air handler was to short. Sort of like only having air in the center of the coil not the edges. He suggested that they be changed when the units were changed. Fortunately for me I moved before the expense was necessary. I did have additional insulation blown into the attic. I added R-19 over the installed R-30. The cooling system improved by about a 1/4 to a 1/3. The electric bill went down at least. Saved the cost of the insulation in 3 months.
Shade screens do help on full sun windows. Best check with the HOA nazi's before purchace.
Ya I was in an HOA only took 6 months of being on the board before I was planning to move. Cute part is the professional management company is now being sued for non preformance.
Unfortunately spending $300k on a home still gets the bottom of the barrel mechinical systems. The only persons making any real money on new homes are the developers. The subs are all the cheapest that they can find, as long as it meets mininium codes.