Terrible two
At the age of 2-4 a child goes through a phase where they learn the notion of authority. Essentially, by now the child is sufficiently intelligent and autonomous to know what they want and how to get it (more or less), but they don't know that some things are impossible, not allowed or simply not suitable at the current moment. They therefore will ignore the parents'/caregivers' objections and insist on their wishes to be fulfilled. This often means being stubborn, crying, throwing things, biting - whatever can make the parents yield. On some occasions parents reach the limits of their patience and situation may escalate.
Consistency
The most important at this stage is that parents and others remain consistent about what is allowed (or when and how). Not only will this help a child to learn faster the limits imposed on them, but it will also give them a feeling that the world is predictable, which is an essential gradient of what is called self-confidence.
Keeping common front
In this respect, it is important that the parents and the others agree on the same demands and rules. In other words, if one parent says "no" or imposes a punishment, the other should play along. If one disagrees, this disagreement should be discussed without the child present, or, at least done openly, so as not to override the other parent decision. This gets more tricky when dealing with the grandparents, who would often allow a lot more than is permitted at home, and parents-grandparents communication is not always the easiest part of (grand) parenting.
Punishment
As I have already mentioned in the comments, physical punishment or humiliation are off limits. This does not mean that everything should be permitted, and that no misfeed should be punished. Rather one should develop a set of punishments of different level, suitable to one's family situation and circumstances. Examples of possible punishments could be:
- Sending the child to their room
- Taking temporarily away a toy (that is the source of a quarrel)
- Refusing/postponing a reward (such as dessert or coveted activity)
- Gently forcing the child to do the necessary things (brushing teeth, washing hands, dressing, etc.)
I stress again the need for consistency - the punishment should be proportional to the gravity of the misdeed. Always employing the maximum punishment would confuse the child of what is really bad, and what is more or less tolerable. Also, do not promise punishments that you know you won't apply - the child will quickly learn to ignore such threats (e g., they know that you would never sell them to the neighbors).
It is important to associate the cause of the punishment and the consequence, and give the child time to understand it. I suggest following these steps:
- Make sure that the child is actually paying attention (e.g., put yourself directly in fron of them or touch them)
- Explain what you expect to be done and what would happen, if they do not obey. (One recommends using "I-language" rather than "you-language" - e.g., "I want you to take off your shoes")
- Give the child time to react (e.g., "five minutes", or "one last time* of the activity, ir simply say that you count till three)
- If the child does not comply, apply the punishment.
Diversion tactics
Sometimes one can avoid a conflict by using distraction tactics. For example:
- democracy - offer two alternatives which really lead to the samw end ("you want to wash your hands in the kitchen or in the bathroom?")
- avoiding temptations - e.g., simply hide summer clothes in winter, if the child is atubbornly tempted to put them day after day.
- offer a reward - e.g., promise a piece of chocolate, if the child eats a few more carrots
- marketing - formulate your demand as an exciting activity (e.g., making soap bubbles while washing hands)
- doing things together - e.g., ranging the toys.
Reasonable expectations
You cannot expect from a child the same level of understanding that we expect from a grown-up person. In particular:
- Give them time. It may take a child ten times longer to put on their clothes than it takes to an adult, but they do it - this is the principal part.
- Avoid complex explanations and complex demands: "I want you to wash your hands" is better at this age than explaining that we wash our hands in order to avoid infections - simply because the child can understand it.
- Stay calm (easier said than done, but certainly pays off)
- Choose your battles wisely. That the child does not eat with their hands or does not put their feet on tge table is not really important at this age - it can be learned later. On the other hand, such things as not beating/biting other children, throwing stuff or eating with dirty hands are not negotiable.