  Argyres-Douglas theories constitute an important class of superconformal
field theories in $4$d. The main focus of this paper is on two infinite
families of such theories, known as $D^b_p(\mathrm{SO}(2N))$ and $(A_m, D_n)$.
We analyze in depth their conformal manifolds. In doing so we encounter several
theories of class $\mathcal{S}$ of twisted $A_{\text{odd}}$, twisted
$A_{\text{even}}$ and twisted $D$ types associated with a sphere with one
twisted irregular puncture and one twisted regular puncture. These models
include $D_p(G)$ theories, with $G$ non-simply-laced algebras. A number of new
properties of such theories are discussed in detail, along with new SCFTs that
arise from partially closing the twisted regular puncture. Moreover, we
systematically present the $3$d mirror theories, also known as the magnetic
quivers, for the $D^b_p(\mathrm{SO}(2N))$ theories, with $p \geq b$, and the
$(A_m, D_n)$ theories, with arbitrary $m$ and $n$. We also discuss the $3$d
reduction and mirror theories of certain $D^b_p(\mathrm{SO}(2N))$ theories,
with $p < b$, where the former arises from gauging topological symmetries of
some $T^\sigma_\rho[\mathrm{SO}(2M)]$ theories that are not manifest in the
Lagrangian description of the latter.
