We present the first simultaneous global QCD analysis of spin-dependent parton distribution functions alongside their spin-averaged counterparts and pion, kaon, and unidentified hadron fragmentation functions. This analysis includes all data relevant for constraining the polarized light quark sea asymmetry $\mathrm{\ensuremath{\Delta}}\overline{u}\ensuremath{-}\mathrm{\ensuremath{\Delta}}\overline{d}$, in particular the latest polarized $W$-lepton production data from the STAR Collaboration at RHIC and semi-inclusive deep inelastic scattering data from COMPASS, allowing the most robust extraction available with minimal theoretical assumptions. We also extract a self-consistent set of antiquark polarization ratios $\mathrm{\ensuremath{\Delta}}\overline{u}/\overline{u}$ and $\mathrm{\ensuremath{\Delta}}\overline{d}/\overline{d}$ and determine the signs of the truncated contributions to the proton spin from the light antiquarks.