We estimate the triplet-singlet relaxation time due to spin-orbit coupling assisted by phonon emission in weakly confined quantum dots. Calculations are performed taking into account Coulomb and spin-orbit interactions exactly within the full configuration interaction method, and Fermi golden rule. Our results for two and four electrons show that different triplet-singlet relaxation trends observed in recent experiments under magnetic fields can be understood within a unified theoretical description, as the result of the competition between spin-orbit coupling and phonon emission efficiency. Moreover, we show that properly designed QD structures may give access to very long-lived triplet states as well as to selective population of the triplet Zeeman sublevels.