Overall, the concept isn't terrible. The main issue I have with it is that the niche for battle mages is absorbed by so many other specs that it becomes difficult to carve a niche large enough to justify its existence. Death Knights, Shaman, Paladins, and even Monks have a lot of this covered. Your sister sword ability for example functions almost exactly like dancing rune blade. Also your fire spec functions almost exactly like frost, only with a different element.
Honestly, the greatest ability ever for a Battle Mage concept already exists in the game, and that mechanic is maelstrom weapon. MW is so simple and genius that it simply doesn't make sense to create a Battle Mage class without outright stealing the concept and re-applying it.
The Arcane spec shows promise though. I like the idea behind it, and think you should utilize that as the basis for your concept and expand it from there. However, I don't think you should call it arcane. You should call it something like Aegis, and just say that it utilizes arcane magic. It also needs to evolve away from mages for it to stand up on its own. Perhaps linking it with Dragons or some other type of force within Azeroth? You should also look into Warcraft lore for inspiration. There are many unused units and heroes from the RTS games to pull inspiration from, as well as NPCs in WoW to get some neat spell ideas. Linking your class concept to Warcraft heroes gives your idea an air of credibility.
However, I just don't see this concept working without something like Maelstrom Weapon. If its just Melee with ranged instant spells, it's no different than the other magic/Melee hybrids already in the game.
I do enjoy a challenge though, so maybe I'll do a write up of this concept to see if I could make it different than other classes in the game.