I am a retired designer of passive solar homes, specializing in sunspaces, but in cold/cloudy climates. A lot of the advice you have already received here is very good, so let me summarize the priorities. First, solar heat is a good thing during the heating season, so don't waste it by venting it to outdoor and then heating your home with costly fossil fuels. The vent to the house was a good thing, so define and solve the problem you have with it, instead of throwing away the venting system including its advantages. The old adage is "Don't throw the baby out with the bath water." In other words, vent the excess sunroom heat (during the heating season) to heat the house in some other way. That may be as simple as leaving the door open during the day, or moving the fan opening to vent the warm air into a different room. Or....is it really a problem to vent the hot air through your daughter's room in the afternoon, during the heating season, when she is probably in school? Is the issue the noise, or the excess heat...both? or neither? To avoid sunroom apparent overheating in winter, and still use it to heat the house, you might use an "interceptor" strategy such as the interior window screens suggested already. What that does is absorb the sunlight, which heats up the dark screen material, which in turn warm air that rises through it, to the ceiling height and can be vented into the house via the circulation fan through the wall. This works like a typical solar air heater, but with a room behind it instead of a wall. During summer, you may use a shade sail or other outdoor strategy to reduce sunlight getting to the windows, and/or also vent the sunspace to outdoors through the east or west walls., (windows or vents). Since you are in new Mexico there are a lot people who understand how passive solar heating works, and have dealt with many of its idiosyncrasies. You can ask around and invite one (or more) over for lunch and a look at your situation. New Mexico is the big passive solar state.
