OK. Prepare for a long response... (sorry!)
Firstly, anger is a human emotion as normal as happiness, sadness and love. So there's nothing inherently wrong with it.
Secondly, I've certainly felt crossness towards my children's behaviour at times, frustration, disappointment very occasionally but never 'anger'.
I admit there's an element of semantics here so, to clarify, to me, anger is a very extreme emotion. Crossness, displeasure, irritation, frustration are all milder emotions. To me. Some situations make us feel angry and we can experience a sense of loss of emotional control. But those should be reserved for the greatest injustices. Not a small child's behaviour (but that's just my take on it).
So, as an emotion, it's perfectly normal, and we can't control the emotional response we have to a situation. But we can control our behaviour - verbal and physical - in response to that emotion (eg you don't have to shag that married man just because you fancy him).
However, I think a lot of people misidentify their emotions because we generally have poor emotional literacy.
Essentially, the physiological response to all emotions is the same and we identify them according to context - excitement on Christmas Eve vs nervousness before an exam - the physiological response is the same). It's one of the reasons why women post on here in really shitty relationships claiming to love their partner. They're certainly feeling a big emotion but is it really love? But we can only identify the emotions we understand.
A lot of anger is actually shame. Shame is the bigger problem. But it's an emotion that isn't really discussed.
As an example, imagine your small child misbehaves in public.
It's a bit irritating because you've had to deal with one tantrum this morning already so you're behind in what you need to do (frustration and pressure of expectation). What makes it worse is that you feel like everyone else is watching you and judging your parenting and you're embarrassed by how your child is behaving (shame). This feels intense and you experience the intense emotion as anger. And the source of that anger as your child.
You feel 'angry' with the child in case other people are watching and you think they're judging you to be a shit parent who can't control their child. So you shout at your child to get them to stop. It doesn't work. The shouting escalates the child's behaviour because your child doesn't have any labels for their emotions. They just feel bad and intensely something. You might find yourself throwing out a threat or two, "If you don't stop... then..." Your child reacts more. They've got no space to calm down. They feel horrible and their safe person is shouting at them.
At this point, everyone has lost it because the parent has misidentified their emotions as anger towards.the child when it's actually frustration and shame. And are trying to manage those feelings in themselves by controlling their child's behaviour. Parent and child are both dysregulated. No one wins and the parent is expecting a degree of emotional control of a child that they don't have themselves (or they wouldn't be feeling so 'angry').
It's far better to acknolwege the initial emotion as frustration (circumstantial) and the second emotion as shame (down to societal expectations) because then it's easier to see, with clarity, that your child is struggling and, actually, it's not appropriate to be 'angry' with them.
It's the same when your child won't give up a toy someome else had first or hits another child. You feel frustrated by their behaviour and shame at how you and your child might be viewed by others/the fact you couldn't stop it.
So, to go back to your question, is 'anger' really what you are feeling or is it something else? And is there a better way of responding than 'showing anger'.
I don't know how well I've explained that. I was trying to keep it short!