smoke comes out from second fireplace.

we have an old house with multi fireplaces too. What I did was to install separate stainless liners in each of the flue areas that we planned on using. (The other fireplaces we had sealed up with a light asbestos cement so that we could open if we wanted.
You should have separate liners to avoid this very thing and to prevent chimney fires.
There are all levels of liner materials from SS to ceramic. Even though ceramic liner materials may be cheaper, it will cost more to install em cause you need a separate cleanout, wheras Stainless allows the chimney sweeps to get in right at the bottom of the flue.

Be careful if you use your fireplace as you describe. You oughta have a CO monitor in the lower room so nobody gets a dose of toxic fumes.

Another issue you might be having is the fireplace requires that house draw in air from somewhere to replace the hot air and smoke going up your chimney. Your house may be so airtight that the only place it can pull in air is through the other fireplace which can pull smoke back down. Try opening a window near the fireplace when you use it and see if that helps the problem. If not then you should follow farmerman's advice.

good point. When we decided which fireplces we would use, we had a mason com in and drill a hole to the outside in the fireplace fire bed. This "hole" was outfitted with a small flue pipe and a controller so we could open or close it and a screened vent on the outside also with a controller.

This keeps warm air from the room going up the chimney. Most of a fireplaces heat is from radiation and then conduction from the heated surfaces (like furniture and rugs). The heated air could be sucked into the fireplace and not give you the desired comfort.

Mot all new fireplaces should have these outside air pipes.

Yes. it helps when i open window near the fireplace. but i can not keep opening window in winter so i plan to extend its chimney about 3ft higher then another chimney and install wind fan on it. what you think?

Youll be sucking the warm air out of the room with a greater efficiency.