  We define parabolic quasi-Coxeter elements in well generated complex
reflection groups. We characterize them in multiple natural ways, and we study
two combinatorial objects associated with them: the collections
$\operatorname{Red}_W(g)$ of reduced reflection factorizations of $g$ and
$\operatorname{RGS}(W,g)$ of the relative generating sets of $g$. We compute
the cardinalities of these sets for large families of parabolic quasi-Coxeter
elements and, in particular, we relate the size $\#\operatorname{Red}_W(g)$
with geometric invariants of Frobenius manifolds. This paper is second in a
series of three; we will rely on many of its results in part III to prove
uniform formulas that enumerate full reflection factorizations of parabolic
quasi-Coxeter elements, generalizing the genus-$0$ Hurwitz numbers.
