Your gal is not having eating disorder. She's just a normal kid who wants to eat everything.
For your MIL, you have to get your husband to cooperate with you. Ask him to talk to his mother. My husband and I stand on the same front when it comes to eating habits for my little ones.
1 thing my hubby did, is to tell my little girl that she is not to eat any junk food and no ice cream etc in front of his relatives. And if we found out that my little girl got to eat junk food and ice cream after that, we will punish her right in front of the relatives who gave her those food. We will appear unreasonable to them but after a while, they will get the message.
I controlled my little girl's diet fully until she's over 2 years old. She had her first ice cream on her 2 yr old birthday and started to have some meat and a little bit more flavor inside her porridge only after 2yrs. I gave her only vegetables like spinach and broccoli etc in her porridge. No salt nor sugar. Everything pure flavored by the vegetables I put inside.
Only until recently then we let her eat fries too.
Thus, I believe you are the mother of your child. You should stand up for your child if you think your MIL is doing the wrong thing. Just smile and tell her you'll think about her suggestion.
Added: Just remember, your MIL loves your little girl too. But like all grandparents, they dotes a lot. You will get there when your child grows up and have kids of their own. It's really different when it comes to your own kids and your own grandkids.