  We extend earlier results on the relation between the dimensionless tunneling
channel conductance $g$ and the fractional Coulomb blockade peak splitting $f$
for two electrostatically equivalent dots connected by an arbitrary number
$N_{\text{ch}}$ of tunneling channels with bandwidths $W$ much larger than the
two-dot differential charging energy $U_{2}$. By calculating $f$ through second
order in $g$ in the limit of weak coupling ($g \rightarrow 0$), we illuminate
the difference in behavior of the large-$N_{\text{ch}}$ and
small-$N_{\text{ch}}$ regimes and make more plausible extrapolation to the
strong-coupling ($g \rightarrow 1$) limit. For the special case of
$N_{\text{ch}}=2$ and strong coupling, we eliminate an apparent ultraviolet
divergence and obtain the next leading term of an expansion in $(1-g)$. We show
that the results we calculate are independent of such band structure details as
the fraction of occupied fermionic single-particle states in the weak-coupling
theory and the nature of the cut-off in the bosonized strong-coupling theory.
The results agree with calculations for metallic junctions in the
$N_{\text{ch}} \rightarrow \infty$ limit and improve the previous good
agreement with recent two-channel experiments.
