  The $^{23}$Na($\alpha,p$)$^{26}$Mg reaction has been identified as having a
significant impact on the nucleosynthesis of several nuclei between Ne and Ti
in type-Ia supernovae, and of $^{23}$Na and $^{26}$Al in massive stars. The
reaction has been subjected to renewed experimental interest recently,
motivated by high uncertainties in early experimental data and in the
statistical Hauser-Feshbach models used in reaction rate compilations. Early
experiments were affected by target deterioration issues and unquantifiable
uncertainties. Three new independent measurements instead are utilizing inverse
kinematics and Rutherford scattering monitoring to resolve this. In this work
we present directly measured angular distributions of the emitted protons to
eliminate a discrepancy in the assumptions made in the recent reaction rate
measurements, which results in cross sections differing by a factor of 3. We
derive a new combined experimental reaction rate for the
$^{23}$Na($\alpha,p$)$^{26}$Mg reaction with a total uncertainty of 30% at
relevant temperatures. Using our new $^{23}$Na($\alpha,p$)$^{26}$Mg rate, the
$^{26}$Al and $^{23}$Na production uncertainty is reduced to within 8%. In
comparison, using the factor of 10 uncertainty previously recommended by the
rate compilation STARLIB, $^{26}$Al and $^{23}$Na production was changing by
more than a factor of 2. In type-Ia supernova conditions, the impact on
production of $^{23}$Na is constrained to within 15%.
