  A relatively hyperbolic group $G$ is said to be QCERF if all finitely
generated relatively quasiconvex subgroups are closed in the profinite topology
on $G$. Assume that $G$ is a QCERF relatively hyperbolic group with double
coset separable (e.g., virtually polycyclic) peripheral subgroups. Given any
two finitely generated relatively quasiconvex subgroups $Q,R \leqslant G$ we
prove the existence of finite index subgroups $Q'\leqslant_f Q$ and $R'
\leqslant_f R$ such that the join $\langle Q',R'\rangle$ is again relatively
quasiconvex in $G$. We then show that, under the minimal necessary hypotheses
on the peripheral subgroups, products of finitely generated relatively
quasiconvex subgroups are closed in the profinite topology on $G$. From this we
obtain the separability of products of finitely generated subgroups for several
classes of groups, including limit groups, Kleinian groups and balanced
fundamental groups of finite graphs of free groups with cyclic edge groups.
