Ok here it goes.
Alright first I am going to explain the difference between our characters and why I made it this way. I mean no disrespect or offense Ms. Yaroki.
I made Mukade fourth seat in your Squadron specifically for the purpose that I know for a fact, that he would have hated Nanashi to the extent that he would have not rested till he slit her throat. The way that Nanashi presents herself as "Kenpachi", Mukade would have found sickening. He literally would have not rested until she was dead. Even if he had to resort to dirty methods. Mukade is a "Sword Artist" therefore the way he thinks and the way your Character thinks are completely two different Ideals. He would have been disgraced and loathed your RPC to a passion. When he is used he will still be disgraced that Nanashi was the previous Kenpachi. He feels that the Soul Society was dishonored by Nanashi and he will personally have slit anyone's throat that dares to remember Nanashi as a previous Kenpachi. A being whom gives up the ways of the sword for another way is just disgraceful and dishonorable for a Kenpachi. In his mind anyway.
However, these ideals do not disgrace Kido itself. Mukade is aware of the grand power that Kido beholds thus he trained up to himself. He does specialize in it. However seeing as Nanashi claims to already have a third seat I had to make a Mukade be your fourth. If in fact he was your Vice, he would have challenged you on a daily basis. He would have snuck in Nanashi's room and slit her throat. Mukade has hated Nanashi from day one because of the creative differences they both share. As you will see when I recreate the whole squadron and from this profile.
Now as for the "no solo training rule". If you read his bio closely, thre is a chapter where Mukade was trained by a unknown shinigami at the time whom is unknown and has gone rouge by the name of "Manazoki". When I stated trained it was an allusion that he would teach him the foundations of everything that was needed to join the Court Guard Squads. Since he did not join any type of academy. So it was alluded that Manazoki taught him the foundation and extend the prowess of Kido.