I'm in 16th century Europe, and dino nuggets haven't been invented yet. What do I feed my children that are picky eaters?

There's always more that can be said, but you may find my answer to a question about a medieval toddler relevant to your interests. I'll defer to historians of childhood in that era but my hunch is that they would be fed whatever their non-picky siblings would be fed. In other words, a child's food preferences wouldn't hold the same weight they hold in the modern era.

Edit: OK! More to say! One of the perks of being a flaired member of AH who is also a mod is I can see the rule-breaking comments removed by other mods on questions I've answered (we don't mod in threads we answer.) And what I can see is a whole lot of people demonstrating what historian's describe as presentism. In effect, it's when we say "X is like this today so X must have been like this in the past." The challenge, to paraphrase /u/Daeres, is basically, we don't have enough evidence to get a full picture of children's eating habits in that period. From a post of theirs on a roundtable on the subject a while back:

To summarise all of this, we do not have the luxury of knowing enough about the ancient world to decide what does and does not resemble the modern world. Nor is it the job of past societies to resemble us, it isn't a failing of theirs that they do not. I find that presentism is often based around making the past service us, making the past 'useful' for us. I think that's a poor approach, and one without empathy despite the aims of presentism. The empathy to recognise that past societies do not have to resemble us in order to have had full, real human lives. We should know the past before we try to throw narratives about its connection to us.

In other words, we can't conclude that children were punished for eating or not eating, if they were picky or not, or the exact dynamics around meal time. Another factor contributing to our inability to reach such firm conclusions is the history of childhood itself is fairly new. To borrow from an answer I gave around children in mines:

Charlotte Hardman, one of the first anthropologists of childhood, wrote in 1971 that the history of children (and women) is "muted." Children and women were, she said, "unperceived or elusive groups (in terms of anyone studying a society)." Hardmen contributed to a field of study known as the sociology of childhood which incorporates history and anthropology into its work and offers a paradigm for thinking about childhood. The relevant features of the paradigm that apply to our understanding of children in history are (from James & Prout, 1997):

Childhood is understood as a social construction. As such it provides an interpretive frame for contextualizing the early years of human life. Childhood, as distinct from biological immaturity, is neither a natural nor universal feature of human groups but appears as a specific structural and cultural component of many societies.

Childhood is a variable of social analysis. It can never be entirely divorced from other variables such as class, gender, or ethnicity. Comparative and cross-cultural analysis reveals a variety of childhoods rather than a single and universal phenomenon.

Children’s social relationships and cultures are worthy of study in their own right, independent of the perspective and concerns of adults.

Children are and must be seen as active in the construction and determination of their own social lives, the lives of those around them and of the societies in which they live. Children are not just the passive subjects of social structures and processes.

Ethnography is a particularly useful methodology for the study of childhood. It allows children a more direct voice and participation in the production of sociological data than is usually possible through experimental or survey styles of research.

An important thing to remember is that when adults wrote things down about what children did or didn't do, it was usually in service to adult goals. It's not that adults lied about children, rather, explicitly writing about children for the purpose of capturing what the child was doing is a fairly new construct. At the same time, historians of childhood, like all historians, are looking at the historical record with new questions and new perspective and are developing new ways to find children themselves in the historical record.