Okay, from a psychological point of view, no, the kids (Yukio and Riruka) were not "mentally disturbed". This coming from me who did 1 year of psychology in university, and Im assuming you never did any. Children who dont receive enough guidance from parents tend to do things their way. As I have mentioned earlier, children do whatever they can to get instant gratification. If they are not guided properly, they would not know the true meaning of satisfaction. And hence, their world will be shaped in a negative way. This is the essence of what we all know as "bad childhood". But most people grow out of it. They snap out of their own delusional world when they are older, by their ownself or with the help of others. Most people have some form of traumatic experience in their childhood. This doesnt mean that most of us are mentally unsound. The point is that we snap out of it. People who are mentally unsound cannot control their emotions and thoughts because they do not realize the situation they are in. In whatever form of the definition, "mentally unsound/disturbed" does not fit the description of the Fullbringers and their past.
From Yukio's point, we obviously can see that he is unhappy of the way things are now. He is unhappy of how he hates everyone. This was pointed out by Hitsugaya. And because thats the only way of life for Yukio, he is now trapped in self-denial because deep down he knows that what Hitsugaya said about him was correct.
From Riruka's point, it wasnt explicitedly mentioned but she was definitely feeling a sense of regret for how she handled issues when she was young. Now she's much older, and she knows that its not right to take things belonging to others as her own. Children steal stuff when they are young. May it be a candy from a store or a friend's pencil. That was Kubo's point about Riruka. Just that because of her abnormal powers, she went a bit extreme. But as I mention again, she snapped out of it. This time round, she did not HIDE Ichigo in her box. She described the Fullbringers' old ways as "stupid". The "horrible thought" of killing someone with her power that didnt cross her mind.. Now has, and she is fully aware of it.
In case anyone wants to make an argument about Riruka stealing Rukia's powers/reiatsu..
Firstly, Rukia's reiatsu is not the thing that she really wants. She is stealing it in order to attain your goals. It's the same logic as how Tsukishima described Byakuya's fight, "you prefer to toy with your enemy, stealing away the things they hold dear".
Secondly, it's not unusual in a shonen manga. Dont tell me all the characters who stole powers in other shonen mangas are psycho.
Machuran said:
It is for no good reason, he just chose to kill his wife out of the blue just to test his powers. At least Light Yagami from Death Note had the decency to test his powers out on criminals before he turned into a power-hungry psycho, Giriko just went psycho and killed her all of the sudden.
Just that Light turned psycho only AFTER he found that his powers worked (as you mentioned). Doesnt justify Giriko's going psycho BEFORE killing because he backed out after killing his wife. Just as the law has different punishment for murder according to the state of mind, it shows that not all murders are mentally unsound. And there's a difference between murder and manslaughter. If it is really the case that Giriko had no hatred towards his wife, I am guessing that Giriko's case is more of a manslaughter. 'Hey I think this is a new power, lets try it out' and lo and behold, his wife appears and boom, she's dead. He probably did have the intent to kill but not the intent to kill his wife, which led to remorse. It just like Im holding a knife, I have no idea what it does but Im guessing it can cut and I wanna try it out. Out comes my friend at that moment and without a second thought, I try the knife on my friend and it does cut. Sometimes the body acts faster than the mind (I know it is literally impossible but it's an expression). There was no ill will towards my friend. Just wrong place and the wrong time.
BUTTTTTTTTTTTT.... That is still not an excuse to kill. Im not trying to defend Giriko's actions. It is a fact that he did have the intent to kill, whether or not the intent is directed towards his wife.
And I say this again, the Fullbringers were probably all 'sweet-talked' into this by Ginjo. Unfortunately, Riruka's recount was interrupted by Rukia. We would have to wait for another time one of them talks about this matter.