Fireplaces, Heating Stoves, Flues and Chimneys - Wood Stove backdrafts

I have a wood stove that was recently installed in our new home. The stove has what appears to be a 6-8 inch pipe flue extending the length of approximately 6-7ft towards the ceiling and is separated from the wall about 2 ft per the construction building codes in out county. The exterior portion of the flue on the pitched roof, has a cap covered by a steel mesh. My question is that on windy days during the winter, we experience some back draft that sets of smoke alarms and leaves a nasty smell for days. What can we do to avoid this from happening? Do we start by changing the flue? The Cap? or consider a different way of removing the smoke such as installing blowers or such? In our old home where this stove was originally installed, the flue was much shorter with a couple of elbows and attached to the wall chimney that also funneled smoke from wood fireplace on the other side of the wall. The brick chimney extended through the roof and there was no cap installed but rather a square 6"X12" opening that never created any form of backdraft. Does anybody have any suggestions on how we can find a simple inexpensive solution to this problem?