Warning, wall of text incoming. this is probably my longest post in this forum so I tried to put sections to make it easier :/
So it's ok to kill your brother as long as he doesn't get burned by fire like yourself then? Well, now it really makes sense.
I didn't say that at all. I was talking about the "gruesome death" part. That was the final test that she willing to give him to see if he truly has it in him to take the iron throne. And he failed.
Death and murder is always a complex subject to decide if its right or wrong, it cannot be done in one single thought. So I think we all need to take a step back and look at things from a holistic point of view.
The situation
First, we need to look at the backstory of these three characters. Viserys has been dreaming of getting back his kingdom since he was a little child. Not only did he want it, it was expected of him. And he was mocked his entire life for something he had no control over. He also had his sister, who was also supposed to be his wife, under his responsibility. They obviously cared for each other, but he treated Dany as an object at his disposal. Viserys found a way to reclaim his kingdom by marrying his sister to the barbaric tribe leader, Drogo, and get his army in return. Despite Dany's discontentment, the marriage was done anyway. What's worse is that her brother basically told her that he'll sell her dignity effortlessly if that's what it took.
The Dothraki is a tribe with very special traditions and culture. Dany manages to deal with her position very quickly, and she even embraced it by accepting her role as the Khalessi of that tribe. She was no longer under her brother's protection, and most certainly not his toy anymore, Visarys however did not see that. He still saw her as his property, and belittled her in every single opportunity that fell upon him. He did not respect her tribe's traditions at all, and he saw himself as a superior to all of them without ever earning their love, respect, or fear. Dany also discovers that she cannot be burned, a trait that she believed was a sign of having true power to get the iron throne back.
Fast forward to the events that took place. Visarys enters the a sacred place of the Dothraki, unsheathed his sword (a blasphemous act for the Dothraki tribe), humilated their traditions, and threatened to kill their Khalessi and the Khal's unborn child. He did this to remind Drogo of his share of the bargain. I give you my sister, you give me the throne, or else. Drogo had had none of that, and answers his threat with a gruesome death. Dany all the while did absolutely nothing to resolve the matter (outside of a few feeble attempts at the beginning), she even held Drogo's hand while she literally translated his words to her brother. And finally she didn't even flinch when he had melting gold on his head.
I think this about covers the events and backstory quite objectively, if you have any objections please raise them. But now we need to look at the overall situation. The very first question we need to ask is "did Viserys need to be punished, under any form?". I think we can all agree that the answer here is yes, but honestly if one objects to this point then please raise it. It will lead to very interesting discussion.
Dany's Involvement
The next point we need to address is Dany's involvement in the matter. Afterall, she was only a passive observer of the events. Did she truly have a choice? Personally, I think the answer to that is yes, but her options nonetheless remain limited. The way I see it, she had three options. 1) Do exactly what she did in the show; Nothing. 2) Warn him of Drogo's intentions. And 3) Attempting to persuade her husband to seek other forms of punishment outside of death. There are no other options that could be deemed ethical if you believe Viserys did deserve punishment.
I think option 2 is rather fruitless, even if she warned him of what's going to happen to him. It wouldn't have changed a single thing, furthermore it wouldn't have calmed viserys down and he probably would have killed Dany if he learned the truth. Nonetheless it would have been more honorable than doing nothing since, as the other poster said, it was trickery (though not in the scale of Joffery, but that is another debate for another time). This leaves the third option, which would have been the ideal solution if we can answer the crucial question. Did Viserys deserve death?
Discussion on death penalty
Before jumping to answer "yes" or "no",here are different points of view that need to be examined. First is we need to look at the consequences of his death. Basically it's the concept of the greater good. Did his death, at that time, benefit people? This point is very much open for discussion, but I think the answer is yes to that one. Khalessi earned her husband's love and her security for both herself and her unborn child at the time. Viserys has been punished before, as was he warned, and it didn't change his behavior at all. An alternative solution would obviously to exile or imprison him. But these wouldn't have respected the traditions of the dothraki, traditions he was very well aware of but didn't even care to understand. Even if they somehow decided to keep him away from his sister. would that be in Dany's best interest? To me, someone who threatens a mother and her son at point blank is definitely a reason to kill.
Why would she let him live?
This leads to the second point of the discussion. The first part was about the practicality of his death. But it doesn't talk about his rights or his value as a human being.
Basically, the right to live without having to earn it.One could say that killing is wrong under any circumstances no matter how brutal the situation is. But if one uses this argument then as their moral compass then other considerations need to be taken as well. Having zero tolerance to unethical behavior then even actions like lying to protect your friend from being murdered, or stealing food because of starvation are also seen as unethical practices. This is why I don't think this moral code can be applied because it simply removes reality from the equation. Talking about rights, Viserys also put the life of others at risk as well. Who's rights supersede the other? Personally I think this is the only argument which can be used to say killing him was wrong. If you have any objections. Please say so.
Regardless of your own conclusions of whether or not his death was warranted. I would like you to assume that it was for the time being, because there is one final point I would like to discuss, and that is the method of murder
Method of Death
FINALLY going back to our debate about the way they killed him. Was it justified? Were there other, better means to kill that son of a bitch? Personally, I think not. The melting pot provided the final test for him to see if he truly is powerful enough to take the kingdom. Of course, logically thinking that is completely insane. But Dany's visions came true at the end. If he died any other way she would never know for sure.
I will never, ever write a post this big again, I guarantee you that. But I hope this shows you how I arrived to my conclusion.