Of course it's OK to open/close vents to control airflow. What do you think those vents are there for, anyway?

But to raise a slightly different aspect here... what kind of a lunatic system does your mother have that has a single control zone (i.e., thermostat) for a three-story house? You are just about guaranteed that anyplace you go in the house you are going to be either too hot or too cold.

In Alaska, the weather conditions are incomparably more extreme than in Virginia (temperatures can vary by 170 degrees F or more summer to winter), and the hvac systems are designed accordingly. My house had two stories, and six separate, individual thermostatically controlled temperature zones. The furnace (no a/c) was a computer-controlled Buderas system that monitored outside air temperature and set the boiler temperature accordingly. The Buderas burned about 25% less fuel for the same size house as a conventional (and far less expensive) system might. See the attached picture. My apologies for the mess, the basement was being remodeled and everything got dumped into the furnace room. The point of this rambling discourse is that I could heat my 3400 square foot house for what most of you would consider a staggering amount of money (average about $3,000 per year) but some of my cow-orkers were spending three times that amount on houses half the size. In Winter time I would frequently have a room 30 degrees colder than the room next to it (all the inside walls had 4" insulation) if I wasn't using that room. No sense in heating empty space! Your mother's system is not only badly designed for comfort, it is badly designed for economy of operation. It's like an ink-jet printer: Cheap to build/buy, expensive to operate.

You may be able to alleviate the problem considerably by judicious adjustment of airflow, but it may turn out to be a continual process as the seasons change.

tanstaafl.