How to eliminate back draft with two stoves

[RSNovi]

I have a Jotul Oslo in the basement and just installed a Jotul C350 insert in my zero clearance fireplace on the main floor. When I burn the 350 I feel a significant draft in the stove. It is can be a very cold draft if it is cold outside.

I think it is combustion air causing the draft and I think it is being pulled through the stove in the basement. I can feel cold air exiting the inlet of the
Oslo while burning the 350 and the stove is ice cold.

Would installing a stovepipe damper in the Oslo eliminate the back draft? Any other ideas?

 

[RSNovi]

One other issue. Since both chimneys are near each other, smoke will get sucked down through the Oslo chimney and into the house. I would like eliminate that as well.