I mean this in all sincerity and love, I was super alarmed by this message pertaining to a 15 month old-but now I see where you're coming from. At first I couldn't believe the carefully measured and unbuttered descriptions of daily food (I don't butter my kids whole grain bread either, but I'm just saying, it seemed notable in context with the half cups and half apples, and dr's perfect 50% weight chart), then when I saw you mention an eating disorder it sort of clicked.
Do not worry about rationing your child's food and don't watch her shape with a magnifying glass. She needs as much healthy food as she will eat. For her brain development and sleep habits. All my kids grew in spurts of "out" and then "up" Chubby one day, longer the next all through toddlerhood. They've always been somewhere totally average on the charts.
They eat no junk food at all, drink only watered down natural juice or organic milk, but they are allowed to eat as much as they want. They have to eat what I feed them for meals, and all the healthy snacks they want. They get a bite or two of cake at birthday parties and a sliver of Halloween chocolate (maybe 1/8 of a mini snickers) with their fruit for dessert for a couple of days after Halloween so junk doesn't become the forbidden fruit. They know what's only for rare occasions like ice cream because of sugar. The more healthy food they get used to liking the better before they get out in the junk food world. They have tons of energy for playing and sleep like stones.
I have no idea of their exact portions from day to day. But kids need natural essential fats for their brains-(olive oil, avocados, almond butter,)and most of all they need to learn not to be too obsessed with food.
Your daughter is so young, you really don't need to worry about a chubby round baby shape.
If you think your MIL may be secretly feeding her excessively fattening snacks with bad oils and sugars and and chemicals and fat in them like Jif or something, you could make sure she isn't. Read the labels on MIL's food and make sure nothing is artificial or sugary. Just worry about quality of food, not quantity. Great job caring about your daughter's health! Keep it up, but don't worry about her eating too much at this age!