  The $\Lambda N$ and $\Sigma N$ interactions are considered at next-to-leading
order in SU(3) chiral effective field theory. Different options for the
low-energy constants that determine the strength of the contact interactions
are explored. Two variants are analysed in detail which yield equivalent
results for $\Lambda N$ and $\Sigma N$ scattering observables but differ in the
strength of the $\Lambda N \to \Sigma N$ transition potential. The influence of
this difference on predictions for light hypernuclei and on the properties of
the $\Lambda$ and $\Sigma$ hyperons in nuclear matter is investigated and
discussed. The effect of the variation in the potential strength of the
$\Lambda N$-$\Sigma N$ coupling (also called $\Lambda -\Sigma$ conversion) is
found to be moderate for the considered $^3_\Lambda \rm H$ and $^4_\Lambda \rm
He$ hypernuclei but sizable in case of the matter properties. Further, the size
of three-body forces and their relation to different approaches to hypernuclear
interactions is discussed.
