Am I misunderstanding or is your horse only receiving 4 flakes of hay a day total?
Personally...if she is, she needs more hay, period.
Alfalfa of not, she needs more hay in front of her and she will gain weight.
I am also unsure of how you are feeding Amplify...but it is not a grain/feed source but it is only to be top-dressing your daily grain/feed ration.
It is a 30% fat nugget and is unpalatable to many horses fed by itself. Also recommended to be started fed in small amounts and build on the amount slowly.
Horses don't normally get "hot" from a cool calorie such as fat.
Yes, there is a protein amount associated with Amplify, but this supplement is normally fed in such small quantities...
Also remember the only way any horse can gain weight is to increase their caloric intake more than they are expending.
If you are working this horse daily, she needs more calories in than out due to that.
Still think to start weight gain by increasing her hay amount fed daily. She doesn't need "alfalfa" only, she just needs to eat more hay of the lesser quality...
I honestly would be looking for a "working lightly" horse to be consuming a minimum of 6-8 good size flakes of quality hay a day...as much as they will eat and clean up, not waste.
If after increasing hay consumption the horse is still not gaining, then look to add additional feed/grain sources of nutrition.
I am also thinking you have already addressed teeth, worms, ulcers and such...
If I misread and misinterpreted your writings, my apologies.