You will need to run a separate duct work system to the second floor if you add a second furnace and AC. It may be very difficult to do this from the basement. It may be more practical to install the furnace in the attic and run a new set of ducts.

I would first see why the current furance is having problems before spending money on a second furnace. The key is to find someone competent.

Agree with Mike.

Have the duct sizing checked out. Undersized ductwork is a likely reason for what she has happening.

"Undersized ductwork is a likely reason for what she has happening."

How about inadequate attic/ceiling insulation? Or air infiltration? Or duct leaks?

It's pretty hard to diagnose from a distance, don't you think?

All of these could be contributing to the problem. I recommend all of these items should be reviewed before you call in a contractor to add a second furnace.