sam2 -does not really sound so shayich. But I saw in halichos shlomo (see tefilah 4 haarah 95 and hilchos pesach by gebroktz) Reb shlomo zalman is mechalek between a minhag, which gets passed down from generation to generation and a personal chumrah, which does not require your children to follow.
His example of a chumra that a son does not need to keep is if one is makpid to not carry in any eruv (not just the ones that rely on rediculous kulos), which is in theory kneged halacha .