That's not the point. Kouichi's mother died BECAUSE of Kouichi, which is exactly why he's so adamant about living a life that she can be proud of; if he doesn't go back and make a life for himself in his own world where she died, it means her death was in vain. It's not about bringing her back, it's about making up for a death that he feels was his fault in the first place.
If he were to stay in this other world, and die in his originally one, then that means his mother died for absolutely nothing... Obviously Kouichi can't just live with that.
Yep! And it makes the choice that much harder cuz you know from that face Caius made he knew what Kouichi was gonna pick ╥﹏╥ other then his growing love for Caius, there is no one more important as Kouichis mother to him.
I might sound insensitive but his mother ain't gonna come back even if he went back so yeah －.－