In the preceding paper (paper I) we examined the decay $\ensuremath{\eta}\ensuremath{\rightarrow}3\ensuremath{\pi}$ in a very general way based on the current algebra of $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ and partial conservation of axial-vector current, but making use of nonlinear chiral Lagrangian techniques. Our results restated the failure of this approach to $\ensuremath{\eta}$ decay which was already known from the work of Sutherland, but in a new, quantitative form which we referred to as the "scale difficulty." In the present paper we continue to apply the same approach, the same techniques, and the same symmetry-breaking model to the same problem. In order to alleviate the scale difficulty, we investigate an extension of the theory in which $\ensuremath{\eta}$ decay is mainly due to a new term which is also contained in the symmetry-breaking $(3,\overline{3})+(\overline{3},3)$ representation. We find, firstly, that the new contribution to $\ensuremath{\eta}$ decay does not alter the good value for the slope. Secondly, using the soft-pion result for $m_{{\ensuremath{\pi}}^{+}}^{2}\ensuremath{-}m_{{\ensuremath{\pi}}^{0}}^{2}$ we can again uniquely determine the phenomenological Lagrangian, and we find that the scale difficulty disappears. Thirdly, we present a simple condition on the symmetry-breaking Lagrangian, plus a speculative test of that condition, that agrees with the new solution. A modification of the tadpole theory of Coleman and Glashow, in which the octet of tadpole mesons belongs to a nonlinear realization of $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$, is explored in the light of the new theory of $\ensuremath{\eta}$ decay. This new tadpole theory, unlike the old, has no difficulty in explaining octet dominance in the weak nonleptonic decays. It also explains why the non non- $(3,\overline{3})+(\overline{3},3)$ part of the pseudoscalar-meson Lagrangian is small compared to the $(3,\overline{3})+(\overline{3},3)$ part, as well as why it is predominantly octet. A new numerical fit to the tadpole theory is presented, which shows that the baryon Lagrangian must also be predominantly $(3,\overline{3})+(\overline{3},3)$.