  We present a detailed, multi-wavelength study of star formation (SF) and AGN
activity in 11 near-infrared (IR) selected, spectroscopically confirmed,
massive ($\gtrsim10^{14}\,\rm{M_{\odot}}$) galaxy clusters at $1<z<1.75$. Using
new, deep $Herschel$/PACS imaging, we characterize the optical to far-IR
spectral energy distributions (SEDs) for IR-luminous cluster galaxies, finding
that they can, on average, be well described by field galaxy templates.
Identification and decomposition of AGN through SED fittings allows us to
include the contribution to cluster SF from AGN host galaxies. We quantify the
star-forming fraction, dust-obscured SF rates (SFRs), and specific-SFRs for
cluster galaxies as a function of cluster-centric radius and redshift. In good
agreement with previous studies, we find that SF in cluster galaxies at
$z\gtrsim1.4$ is largely consistent with field galaxies at similar epochs,
indicating an era before significant quenching in the cluster cores
($r<0.5\,$Mpc). This is followed by a transition to lower SF activity as
environmental quenching dominates by $z\sim1$. Enhanced SFRs are found in lower
mass ($10.1< \log \rm{M_{\star}}/\rm{M_{\odot}}<10.8$) cluster galaxies. We
find significant variation in SF from cluster-to-cluster within our uniformly
selected sample, indicating that caution should be taken when evaluating
individual clusters. We examine AGN in clusters from $z=0.5-2$, finding an
excess AGN fraction at $z\gtrsim1$, suggesting environmental triggering of AGN
during this epoch. We argue that our results $-$ a transition from field-like
to quenched SF, enhanced SF in lower mass galaxies in the cluster cores, and
excess AGN $-$ are consistent with a co-evolution between SF and AGN in
clusters and an increased merger rate in massive haloes at high redshift.
