Schreier theorem on groups which split over free abelian groups

Let $G$ be either a free product with amalgamation $A *_C B$ or an HNN group $A *_C,$ where $C$ is isomorphic to a free abelian group of finite rank. Suppose that both $A$ and $B$ have no nontrivial, finitely generated, normal subgroups of infinite indices. We show that if $G$ contains a finitely generated normal subgroup $N$ which is neither contained in $C$ nor free, then the index of $N$ in $G$ is finite. Further, as an application of this result, we show that the fundamental group of a torus sum of $3$-manifolds $M_1$ and $M_2$, the interiors of which admit hyperbolic structures, have no nontrivial, finitely generated, nonfree, normal subgroup of infinite index if each of $M_1$ and $M_2$ has at least one nontorus boundary.