2007 Ford 500
My grandmother's car will only go 25mph while pulling 3000 rpm. My mom thinks its the transmission. The car has also had an overheating problem lately. She has to add antifreeze/coolant every 3 days or so but there are no obvious signs of leakage. The car also overheats if stationary for too long regardless of fluid levels.

Sounds very serious. Things that will help get you the answers you need.

1st - Find a Ford internet site that specializes in the 500.
2nd - Give them complete details of car (engine, transmission, mileage)
3rd - Give them complete details of each problem.

Antifreeze loss with no leaking could mean it is going into engine somewhere (blown headgasket)?

Is your grandmother one of those two-footed drivers?
You know - one foot on the gas, and the other on the brake.
Tell her to take her foot off the brake pedal.
And also to shut her turn signal off. It's been on for the past 5 miles!