  The discovery of planets in binaries is one the most interesting outcomes of
planetary research. With the growing number of discoveries has also grown the
interest on describing their formation, long-term evolution and potential
habitability. In this work we revisit the dynamics of planets in S-type binary
systems. For that purpose we develop explicit formulas for the secularized
octupolar Hamiltonian, coupled with general relativistic corrections and
non-conservative interactions. We implemented those formulas in an open-source
package \texttt{SecDev3B}, that can be used to reproduce our results or test
improved versions of the models. In order to test it, we study the long-term
dynamical evolution of S-type binary planets during the pre-main-sequence phase
of stellar evolution. During that phase, stellar radius significantly changes
in timescales similar to secular timescales. We hypothesize that when
close-encounters between the planet and its host star happens (e.g. via
Lidov-Kozai effect), particularities in the secular formalism plus changes in
stellar radius may alter significantly the dynamical evolution. We study the
well-known binary planet HD 80606b and found that an octupolar expansion of the
conservative Hamiltonian is required to properly predict its dynamical
evolution. We also apply the dynamical model, enriched with results coming from
stellar evolutionary models, to demonstrate that in S-type systems around
low-mass stars, with relative high inclinations ($\itot\ge 60^\circ$), moderate
eccentricities ($0.2\le e\le 0.4$) and planets located around 1 AU, the
evolution of stellar radius during the first few hundreds of Myr, alters
significantly the timescales of dynamical evolution.
