  We study a strongly interacting "quantum dot 1" and a weakly interacting "dot
2" connected in parallel to metallic leads. Gate voltages can drive the system
between Kondo-quenched and non-Kondo free-moment phases separated by
Kosterlitz-Thouless quantum phase transitions. Away from the immediate vicinity
of the quantum phase transitions, the physical properties retain signatures of
first-order transitions found previously to arise when dot 2 is strictly
noninteracting. As interactions in dot 2 become stronger relative to the
dot-lead coupling, the free moment in the non-Kondo phase evolves smoothly from
an isolated spin-one-half in dot 1 to a many-body doublet arising from the
incomplete Kondo compensation by the leads of a combined dot spin-one. These
limits, which feature very different spin correlations between dot and lead
electrons, can be distinguished by weak-bias conductance measurements performed
at finite temperatures.
