Help with an older trane unit.

Backround: I'm 16, live in NY (lower Hudson valley) with my family. We have a forced air system with an air conditioner outside + air handler inside for cooling and natural gas furnace for heating. (To my knowledge). all units are trane, probably 20+ years old, possibly original to the house, built in late 70's. House is approx 3500 sqft. Units are 4 ton, possibly put in before garage was converted to living space and added to system(all done before we moved in). Siding/exterior insulation recently redone. Roof insulation original to house. No dampers or inline fans to my knowledge, except one large dampner in the main trunk that we have taped open because it squeaks like hell otherwise.

The Problem: During the winter months heating works perfectly, all rooms in the house consistently at 70° no problem, rarely turns on. During the summer, as soon as outdoor temps go over 85° the indoor house temps basically follow the outdoor temps minus about 5 degrees. This has been occuring ever since we been in the house (15 years) my father (by no means an HVAC tech, I probably know more than him from just lurking in this sub) has attributed it to undersized unit and ignores it, to the rest of the family's detriment for 4 months out of the year. My questions is, is he correct in assuming it's just an undersized unit or is something else at play here. If it is just undersized would anyone be able to give me a super ball park quote on installing a new system so I can do a bit of convincing, as my dad refuses to even get a free consultation from trane as he "has no problems with sweating a bit". Thanks, sorry for the lengthy post, I'll try to add some pictures when I have a chance