We investigate the range R_T of the diffusive biased walk X on a Galton-Watson tree T in random environment, that is to say the sub-tree of T of all distinct vertices visited by this walk up to the time T. We study the volume of the range with constraints and more precisely the number of k-tuples (k ≥ 2) of distinct vertices in this sub-tree, in small generations and satisfying an hereditary condition. A special attention is paid to the vertices visited during distinct excursions of X above the root of the Galton-Watson tree as we observe they give the major contribution to this range. As an application, we study the genealogy of k ≥ 2 distinct vertices of the tree R_T picked uniformly from those in small generations. It turns out that two or more vertices among them share a common ancestor for the last time in the remote past. We also point out an hereditary character in their genealogical tree due to the random environment.