Amplitudes derived from scattering data on elementary targets are basic inputs to neutrino-nucleus cross section predictions. A prominent example is the isovector axial nucleon form factor, $F_A(q^2)$, which controls charged current signal processes at accelerator-based neutrino oscillation experiments. Previous extractions of $F_A$ from neutrino-deuteron scattering data rely on a dipole shape assumption that introduces an unquantified error. A new analysis of world data for neutrino-deuteron scattering is performed using a model-independent, and systematically improvable, representation of $F_A$. A complete error budget for the nucleon isovector axial radius leads to $r_A^2=0.46(22) ,{rm fm}^2$, with a much larger uncertainty than determined in the original analyses. The quasielastic neutrino-neutron cross section is determined as $sigma( u_mu n to mu^- p)big|_{E_ u =1,{rm GeV}} = 10.1(0.9) times 10^{-39}{rm cm}^2$. The propagation of nucleon-level constraints and uncertainties to nuclear cross sections is illustrated using MINERvA data and the GENIE event generator. These techniques can be readily extended to other amplitudes and processes.
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