"So (speaking a bit like a mathematician), there is a the system in which you have "trust that there is a wisdom" that you don't (yet) understand. In that system, is there suffering because God does not have the power to prevent it? Or does He let it happen because it's good for us in the long run? Or does He make it happen because it's necessary for our development? Only in the first of these frameworks would there be room for God to be angry." ~Anonymous
I have found this difficult to find an answer because I imagine that there are quite a few presuppositions that we view differently. But instead of trying to get into all of those, I'm just going to answer your direct question the best I can (and let's all keep in mind that I am no expert and that "the experts" have been trying to answer these questions for quite some time. So ultimately, my answer is, I don't know if I have the right answer).
1. "is there suffering because God does not have the power to prevent it?" No, that is not what I believe. I believe that God is omnipotent, so He has all power, which (I believe) is shown through miracles.
2. "Does He let is happen because it's good for us in the long run?" Yes? and no?
So, I believe that there are some kinds of suffering that are good for us in the long run, and I don't want to get too specific about what kinds those are because I honestly think that might be different for everyone. Comparing God to a parent, some examples might be vaccines or medicines or medical interventions that cause suffering. Other kinds of "suffering" are widely accepted as building character- running sprints, lifting weights, delayed gratification etc.
I believe that there are some kinds of suffering that are the result of our choices or others' choices. Some of these can be more severe or traumatic than the ones I mentioned above. Could God intervene and prevent the suffering caused by consequences? I believe that He could but that He chooses not to. Again speaking as a parent, "natural consequences" are a powerful teaching tool for my children to learn to do or not do certain things (and that is not a strictly Christian viewpoint either. It's one of the few consequences that gentle parenting philosophies recommend. See Positive Discipline for more on that).
I say it's a no because sometimes I think God doesn't want suffering to happen but allows it to happen because He values humanity's freedom to choose high enough to allow suffering and not because He wants to teach us something. However, I believe that God can redeem all of those things and use them after they have occurred. (the widely quoted "God works all things together for the good of those who love Him." which I do not believe means everything's going to be hunky dory if you just love God. I think it applies more in this context. Everything that has happened to a person, God can work for good.)
3. "Does He make it happen because it's necessary for our development?" Yes to this one too. But only under specific circumstances. This may be an unpopular view, but I find it difficult to read the Old Testament without seeing a recurring motif. Israel forgets about God and starts worshipping idols. So God allows something bad to happen, or sometimes even causes something bad to happen so that they will remember Him and come back into obedience. In Joel, there's a long list of maladies that happen to the Israelites with the context being that God is trying to call his people back to repentance, but I think it's condensed by this one verse "I will restore to you the years that the locust has eaten, the cankerworm, and the caterpiller, and the palmerworm, my great army which I sent among you."(Joel 2:25). Aside from the humor I find in God calling these bugs His great army, I think it's pretty clear that God is taking responsibility for this plague (which caused famine). Even in claiming that responsibility, God expresses a plan to restore the damage. The books of Joel and Amos would be fairly short examples of what I'm trying to reference here. Are these my favorite and most comfortable stories and ideas about God? No, not really. But there is something comforting about the idea that God will pursue me (not control me) when I pursue evil. I have no idea how often this happens in our current life, but it seemed to happen about every other generation for the Israelites!
To address your final statement "Only in the first of these frameworks would there be room for God to be angry": I disagree. If suffering is a natural consequence of poor choices, then I think God can be angry that the poor choice occurred, and in my view, is angry with and for us that the consequences are painful. And when the suffering is the result of someone else's poor, or even evil, choice, I think God can be angry for the victim and at the perpetrator. (I'm aware that their is a whole additional conversation about free will and sovereignty etc. But for now, I'll just say that I believe God values free will, and that free will results in negative consequences. John Milton says that man is "free to fall, sufficient to stand" or something like that, which is to say, God created humanity with the ability to choose evil and the ability to resist it).
Even if God chooses to allow evil or even to inflict suffering, I think he can still be angry. A doctor may choose to inflict great suffering on a cancer patient to remove the cancer. I believe he or she still has room to be angry at the suffering the treatment causes. And in the case of God causing suffering necessary for our development, perhaps angry is not the right word. Perhaps empathetic would work better.
I feel that my answer has gotten a bit messy. To summarize, I think there are different kinds of suffering and that some of those are allowed by God, and a few very specific ones are inflicted by God. In some of those scenarios, I think God does have room to be angry. In the final one, perhaps God does not have room to be angry at the suffering (I think He's pretty clear that he's angry at the disobedience of the Israelites in my example), but I believe he does empathize with those who are suffering.
Ultimately, I think any discussion of God allowing or causing suffering has be brought back to the idea that God voluntarily suffered and died on the cross to "correct" the mathematical system that required a sacrifice to be suffered that we could not endure. Whenever I am experiencing my own suffering, I am reminded that God is not asking me to experience anything that He has not already suffered.
I will add from my original post that much of my anger is, in fact, directed towards the consequences of peoples' freedom to choose evil. I ponder what kind of system it would have to be to prevent people from choosing evil. Ultimately, people would not be able to choose. Or perhaps cause and effect could be divorced- allow people to make bad choices but remove the ill effects. However, I feel that would be a disservice to the one making bad choices (see A Picture of Dorian Gray for a fictional exploration of how Oscar Wilde imagined that working out). *Edit to add: A friend shared this quote, and I think it's beautiful and relevant:
― Wendell Berry, Jayber Crow
“Christ did not descend from the cross except into the grave. And why not otherwise? Wouldn’t it have put fine comical expressions on the faces of the scribes and chief priests and the soldiers if at that moment He had come down in power and glory? Why didn’t He do it? Why hasn’t He done it at any one of a thousand good times between then and now?
I knew the answer. I knew it a long time before I could admit it, for all the suffering of the world is in it. He didn’t, He hasn’t, because from the moment He did, He would be the absolute tyrant of the world and we would be His slaves. Even those who hated Him and hated one another and hated their own souls would have to believe in Him then. From that moment the possibility that we might be bound to Him and He to us and us to one another by love forever would be ended.
And so, I thought, He must forebear to reveal His power and glory by presenting Himself as Himself, and must be present only in the ordinary miracle of the existence of His creatures. Those who wish to see Him must see Him in the poor, the hungry, the hurt, the wordless creatures, the groaning and travailing beautiful world.”
― Wendell Berry, Jayber Crow
Finally, I will reiterate that I believe this is a "not yet" system. I think that there is some suffering that goes unredeemed in this life, and that feels the most tragic to me, but I tend to think that's because I can't imagine how it will work out after this life (that's a big one of those presuppositions I mentioned at the beginning). Paul writes in the New Testament that if Christ is not risen from the dead, we (Christians) are the most miserable people of all, and I think that applies to this belief that suffering can be redeemed, miraculously, by the resurrection from the dead.
My apologies if that got way too mystical at the end there.

