  We calculate the frequency-dependent admittance of a phase-biased Josephson
junction spanning a magnetic impurity or a spinful Coulomb-blockaded quantum
dot. The local magnetic moment gives rise to Yu-Shiba-Rusinov bound states,
which govern the sub-gap absorption as well as the inductive response. We model
the system by a superconducting spin-polarized exchange-cotunnel junction and
calculate the linear current response to an AC bias voltage, including its
dependence on phase bias as well as particle-hole, and source-drain coupling
asymmetry. The corresponding inductive admittance is analyzed and compared to
results of a zero-bandwidth, as well as an infinite-gap approximation to the
superconducting Anderson model. All three approaches capture the
interaction-induced $0-\pi$ transition, which is reflected as a discontinuity
in the adiabatic inductive response.
