I actually already did most of them, have no idea what to do in the gym, there is no special option with her as far as I can see.
I already increased her love and affection stats and maxed them out yet she doesn't tell me her waist size, I can send screen grabs of her answer when I ask for her waist size....
Have you looked at your phone's quest screen which literally walks you through every step of what to do with Amy(move your cursor around the quest, it gives different tool tips for every step)? Did you change her stats via the console menu, cause that will probably break everything.
The events with Amy go in this order-
do the four workouts.(she needs to bring up working out, aka give you the quest before the next step works which she should do when you talk to her in the gym.)
Talk to her at her room around dinner time.
She wants protein shakes that taste good.
You ask Jennifer(gym only) about the shake, two days must pass
Talk to reception, buy the shake
Gift shake to Amy
Increase stats
Talk to her at her room around dinner time.
She asks for clothes
You ask Jennifer(gym only) about the clothes
You go to Amy's room to talk about measurements.
Done. You have her measurements for both of her outfits.
The shake events might be after the clothes, can't remember. That should be right though.