  The central density profiles in dwarf galaxy halos depend strongly on the
nature of dark matter. Recently, in Malhan et al. (2021), we employed N-body
simulations to show that the cuspy cold dark matter (CDM) subhalos predicted by
cosmological simulations can be differentiated from cored subhalos using the
properties of accreted globular cluster (GC) streams since these GCs experience
tidal stripping within their parent halos prior to accretion onto the Milky
Way. We previously found that clusters that are accreted within cuspy subhalos
produce streams with larger physical widths and higher dispersions in
line-of-sight velocity and angular momentum than streams that are accreted
within cored subhalos. Here, we use the same suite of simulations to
demonstrate that the dispersion in the tangential velocities of streams
($\sigma_{v_\mathrm{Tan}}$) is also sensitive to the central DM density
profiles of their parent dwarfs and GCs that were accreted from: cuspy subhalos
produce streams with larger $\sigma_{v_\mathrm{Tan}}$ than those accreted
inside cored subhalos. Using Gaia EDR3 observations of multiple GC streams we
compare their $\sigma_{v_\mathrm{Tan}}$ values with simulations. The measured
$\sigma_{v_\mathrm{Tan}}$ values are consistent with both an ``in situ'' origin
and with accretion inside cored subhalos of $M\sim 10^{8-9}M_{\odot}$ (or very
low-mass cuspy subhalos of mass $\sim 10^8M_{\odot}$). Despite the large
current uncertainties in $\sigma_{v_\mathrm{Tan}}$, we find a low probability
that any of the progenitor GCs were accreted from cuspy subhalos of $M_{\rm
subhalo}\buildrel > \over \sim$ $10^9 M_{\odot}$. The uncertainties on Gaia
tangential velocity measurements are expected to decrease in future and will
allow for stronger constraints on subhalo DM density profiles.
