The recent observation of Coherent Elastic Neutrino Nucleus Scattering
(CE{\nu}NS) with neutrinos from pion decay at rest ({\pi}-DAR) sources by the
COHERENT Collaboration has raised interest in this process in the search for
new physics. Unfortunately, current uncertainties in the determination of
nuclear parameters relevant to those processes can hide new physics effects.
This is not the case for processes involving lower-energy neutrino sources such
as nuclear reactors. Note, however, that a CE{\nu}NS measurement with reactor
neutrinos depends largely on the determination of the quenching factor, making
its observation more challenging. In the upcoming years, once this signal is
confirmed, a combined analysis of {\pi}-DAR and reactor CE{\nu}NS experiments
will be very useful to probe particle and nuclear physics, with a reduced
dependence on the nuclear uncertainties. In this work, we explore this idea by
simultaneously testing the sensitivity of current and future CE{\nu}NS
experiments to neutrino non-standard interactions (NSI) and the neutron root
mean square (rms) radius, considering different neutrino sources as well as
several detection materials. We show how the interplay between future reactor
and accelerator CE{\nu}NS experiments can help to get robust constraints on the
neutron rms, and to break degeneracies between the NSI parameters. Our forecast
could be used as a guide to optimize the experimental sensitivity to the
parameters under study.Comment: 18 pages, 11 figure