Ankles!
Little humans (kids) have great mobility in their ankles, hips, and shoulders.
Big humans (adults) generally have poor ankle/hip/shoulder mobility. The body compensates by doing more with the knees, back, and neck. Hence the preponderance of back problems, knee problems, neck problems.
Everyone has unique bio-mechanics but sounds like your trainer started off diligently.
Goblet squats are a good way to groove and re-train the squat pattern in adults with bad mobility. Dr. John Rusin, a physical therapist, has quite a few easy to understand articles on his site. Here's one on goblet squats.
https://drjohnrusin.com/goblet-squat-variations/
Other good people to learn from are Eric Cressey (uses a bit more technical language) and Ben Bruno. Not a mutually exclusive list though by any means!
https://ericcressey.com/?s=squat
https://www.instagram.com/benbrunotraining/?hl=en
http://benbruno.com/