First, I am very glad to see you here. You need outside input to prevent more ripoffs. There are a lot of good people here with a lot of experience. Let the opinions develop for a while -- you'll eventually get a great outcome.
Second, some details on the house would help. How large is the footprint of the house, the basement? A 2nd story? The numbers you give suggests a 36x72 house . . . With only 2600 sq ft, a single furnace/AC unit should work unless there are structural issues with air distribution and returns. I had a house that size in VA and one unit worked just fine despite humidity and cold. While I am not a HVAC guy, I am beginning to wonder . . .
Third, how did you find those two HVAC contractors? When the 2nd guy came, did you volunteer the information about adding a 2nd HVAC unit or did he just come up with that idea by himself? The less you say, the better. The calculation should be based on the load requirements of the house . . . not the conrtactor's desire for a new boat.
Fourth, maybe Mom needs a space heater so you don't design a whole house system around her need for heat?
Fifth, does solar electric work in your area? In our area, if your electricity bill exceeds $80 a month, they can provide a system that sends power BACK ONTO THE GRID, so your bill averages $5.00 a month . . . yess, five dollars a month.
Be patient . . . Help is on the way.