  This article introduces a new transcription, change point localization, and
mesh refinement scheme for direct optimization-based solutions and for uniform
approximation of optimal control trajectories associated with a class of
nonlinear constrained optimal control problems (OCPs). The base transcription
algorithm for which we establish the refinement algorithm is a $\textit{direct
multiple shooting technique}$ -- $\mathsf{QuITO}$ $\textsf{v.2}$
(Quasi-Interpolation based Trajectory Optimization). The mesh refinement
technique consists of two steps -- localization of certain irregular regions in
an optimal control trajectory via wavelets, followed by a targeted
$h$-refinement approach around such regions of irregularity. Theoretical
approximation guarantees on uniform grids are presented for optimal controls
with certain regularity properties along with guarantees of localization of
change points by wavelet transform. Numerical illustrations are provided for
control profiles involving discontinuities to show the effectiveness of the
localization and refinement strategy. We also announce and make freely
available a new software package developed based on $\mathsf{QuITO}$
$\textsf{v.2}$ along with its functionalities to make the article complete.
