You are right. Your sister’s four-year-old has learned that if she is persistent, she will get what she wants.
I encourage parents to provide regular meal times and regular snack times for children. Snacks should be provided about two to three hours after meals. Offer appropriate foods during those times. Encourage children to taste each food offered at mealtimes and show them by your example, a bite of each food, especially vegetables. Never force children to sit at the table until they have cleaned their plates or have eaten all of a disliked food.
Allow an appropriate amount of time for the child to eat (30 minutes maximum). When more food is ending up outside the child than inside, remove the food. Don’t offer other food if the child refuses to eat. Children learn that if they hold out long enough that mom will give in to their demands. Remember children will eat if they are hungry. Some exceptions to these guidelines are sick or underweight children. They should be offered food more often or as desired, especially their favorite foods.
Your niece will learn that she will have to eat at meal time or go hungry until snack time. Kids learn that Mom may say no the first 9 times, but the 10th time she says yes. Your sister will have to be consistent to change her habit of giving into her daughter.