Summary: Let \(\Gamma\) be a connected, triangle-free, planar graph with at least five vertices that has no separating vertices or edges. If the graph \(\Gamma\) is \(\mathcal{CFS}\), we prove that the right-angled Coxeter group \(G_\Gamma\) is virtually a Seifert manifold group or virtually a graph manifold group and we give a complete quasi-isometry classification of these groups. Furthermore, we prove that \(G_\Gamma\) is hyperbolic relative to a collection of \(\mathcal{CFS}\) right-angled Coxeter subgroups of \(G_\Gamma\). Consequently, the divergence of \(G_\Gamma\) is linear, quadratic or exponential. We also generalize right-angled Coxeter groups which are virtually graph manifold groups to certain high-dimensional right-angled Coxeter groups (our families exist in every dimension) and study the coarse geometry of this collection. We prove that strongly quasiconvex, torsion-free, infinite-index subgroups in certain graph of groups are free and we apply this result to our right-angled Coxeter groups.