It seems to me that there are really two things here:
- How do you feel about the situation?
- How to address the situation?
While I'd agree that one's emotional state is one's own, and one's outward actions are the more important aspect, I am puzzled by the descriptions of your own emotional states. You describe progressively more intense degrees of anger, and while I understand that people get angry for a variety of things and it's not fair to dismiss their anger as illegitimate, it does seem to me that you would be well-served by framing your situation at least in part with respect to exploring how to avoid the feelings of anger altogether.
Taking your example in order,
A. Why should it concern you at all whether the shirt is on backwards or not? It's well and good to point out the discrepancy, in case the child did it accidentally. But if they claim to have put the shirt on backwards intentionally, I don't see the harm in allowing them to do so, never mind do I see any reason to feel any anger about the situation (however slight).
If there is any negative consequence to be had for wearing a shirt backwards (for example, perhaps the child's peers will laugh at him), the child will find that out soon enough. Either they will care about it or they will not, and they will take that into account in the future. This doesn't seem like something a parent needs to be concerned about. The chances that the child would ever actually be harmed by wearing their shirt backwards seems pretty remote to me.
B. Why should the child's failure to remember a road induce anger? Human memory is fallible. If the child claims to not remember the road, it seems entirely possible that they in fact do not. It seems to me that an appropriate response would be simply to explain to the child that it's not unusual for a person to forget something, or even to "remember" something that didn't happen. I.e. accept their claim as valid, and then help them understand why they may still be incorrect about their conclusion, in spite of their strongly-held belief. Keeping in mind that the goal here is not to change their mind, but rather to give them the tools necessary for them to be able change their mind on their own, eventually, and to accept that it is possible for their own beliefs to sometimes conflict with reality.
(Personal anecdote: as a child, I very frequently had a lot of trouble remembering roads. They all looked the same to me. Highways especially, but often other types of roads. Even if I recognized a particular road as part of a particular route, I would often be unable to recognize which direction on the road we were traveling. Fact is, while I'm much better at navigating today, I will admit that many roads, especially limited-access highways, still look pretty much the same to me. It's only by virtue of being involved in the navigation that I'm able to recognize where I actually am, based on where I've been and what direction I'm traveling. I'm sure there are lots of roads where if I were to be dropped down in the middle of it, I couldn't tell you which road I was on.)
C. This situation seems the closest to one that I could understand why it might induce anger. But only if I make the assumption that the child is not genuinely mistaken about the facts, but instead is just acting like they are in order to achieve some other purpose (such as invoking anger). It seems to me that the saying "never attribute to malice that which can be explained by incompetence" applies. Whatever goal the child may or may not have in mind, you can remain in control of that outcome. It's possible in that situation to give the child the benefit of the doubt with respect to what they believe, to simply state the facts, ask the child why they feel that the facts are not as you claim, and have a reasoned, rational discussion about that.
The fact is, believing something to be true is no way to guide one's actions. If all the child can say is that they believe that there's no practice, that's not a reason and should not be legitimized. Instead, you can simply point out that the calendar is an objective and observable fact that you will be basing your actions on (e.g. taking the child to practice). If the child has some other objective, observable fact that conflicts, then you can have a discussion about which facts seem more reliable. Otherwise, you can make it clear you'll act only on the facts that are known, not on some arbitrarily held belief.
Ultimately, you (as the parent) can make the decision as to whether practice will be attended or not. If you arrive and find out that your facts were in error, you can calmly recognize and apologize for misunderstanding. If your child's facts were in error, you can ask them to do the same (keeping in mind that it's not possible to force a sincere apology out of someone).
Bottom line: I really am not seeing how anger comes into any of these situations. Part of the solution, it seems to me, would be to do some introspection to consider whether an angry response really is warranted, and if you agree that it's not, investigate ways to take your anger response into your own hands, eliminating it from these kinds of situations.
As for how to address each situation, I hope that the suggestions called out in each of the examples above are useful. As a more general rule, it's been my experience as a parent that staying focused on obligations, outcomes, and consequences is the most productive. That is, provide the children with clearly-stated non-arbitrary obligations (i.e. there should be a rational, clearly-stated justification for any obligation), expected outcomes (i.e. what behavior will satisfy the obligation), and consequences for failing to meet the obligation. There's no reason for anger to play a part in any of that.
Of course, it's always important to use positive reinforcement, encouraging the behaviors you want to see. This is ideal. But when negative reinforcement is needed, it typically can and should be dealt with without an angry response, in an objective and fair way. In none of the examples that you cited do I see a reason to be angry about the situation, and only in the third does it even seem like there's any potential reason to act contrary to the child's own intent (and even then, it would simply be a matter of "well, get in the car, we're going to practice"…there's no punishment per se necessary).
(Aside: the above notwithstanding, I recognize that an angry response — i.e. outward expression of anger — can in fact be an effective tool for discipline. And whether or not it's useful or desirable, it does happen from time to time. But it's my opinion that it should be avoided as much as possible. Acting out of anger often leads to the wrong actions, and habitually responding to conflict angrily then teaches that to the child as the response, which makes it harder for them to deal with conflict in productive ways.)