  We present a unifying framework in which both the $\nu$-Tamari lattice,
introduced by Pr\'eville-Ratelle and Viennot, and principal order ideals in
Young's lattice indexed by lattice paths $\nu$, are realized as the dual graphs
of two combinatorially striking triangulations of a family of flow polytopes
which we call the $\nu$-caracol flow polytopes. The first triangulation gives a
new geometric realization of the $\nu$-Tamari complex introduced by Ceballos,
Padrol and Sarmiento. We use the second triangulation to show that the
$h^*$-vector of the $\nu$-caracol flow polytope is given by the $\nu$-Narayana
numbers, extending a result of M\'esz\'aros when $\nu$ is a staircase lattice
path. Our work generalizes and unifies results on the dual structure of two
subdivisions of a polytope studied by Pitman and Stanley.
