The trainer at the Y is a dumbass. Tell him to start teaching aerobics until he gets an NSCA cert.
If you can't squat to parallel, you're not squatting.
The best way to learn to sit back is set a broom stick in the rack, set your feet (toes) just behind the broom stick, start with no weight and learn proper form squatting to parallel.
The smith is OK to start, I still use it with a few clients, but I have yet to find anyone that with the proper guidance, can't squat with a bar. Avoid the smith if possible for squats.
I use a box, but never have my clients sit on it. Too much risk for injury unless you really know what you're doing. Too many want to relax on or bounce off the box. Both will crush the spine.
Usually we finish with a set below parallel, nearly an olympic style squat to build strength in the hole.
W6