In this work we extend the Dune solver library with another grid interface to the open-source p4est software. While Dune already supports about a dozen different mesh implementations through its mesh interface Dune-Grid, we undertake this new coupling effort in order to inherit p4est's practically unlimited MPI scalability as well as its relatively thin data structures, and its native support for multi-block (forest) mesh topologies in both 2D and 3D. The presented implementation is compared to an existing implementation based on Dune-ALUGrid for a variety of challenging test examples in a parallel environment. The numerical experiments show that the implementation presented here is outperforming Dune-ALUGrid in terms of scalability. In addition, an alternative balancing strategy is presented to ensure 2:1 balancing across element faces showing improved performance compared to the existing p4est balance strategy in the numerical examples considered in this work.