OK just for perspective…
About why it works: garelik girl on shlichus in Italy attended a bayis Yaakov where the teacher asked this question and embellished with a mashal. Even if your Yiddishkeit is very warm and strong, like hot water, if you put the hot water in a bowl of cold water and add much more child water than hot, the water gets cold.
Garelik girl answered that yes it’s true but only if the pot is not plugged in. If it is, then the cold water also warms up…that’s the secret of hiskashrus. I heard this story from her brother Rabbi garelik of Crown heights.
On the opposite note, I heard this story but not first hand so could be the details area somewhat off.
Basically a shlucha wrote an upset angry letter to the Rebbe asking why get kids didn’t turn out so well, when the Rebbe guaranteed shluchims children. The Rebbe responded something to the effect of, I never asked you to put those magazines in the bathroom…
Point being if you are on shlichus as a proper chossid and behave as the Rebbe wants, and keep the hiskashrus strong, you’re kids come out all the better. I know many shluchims kids myself, when their parents are chassidim they’re the cream of the crop of lubavitch. Here neville you are mistaken. There are many many case studies of living second generation shluchim today.
But if someone goes on “shlichus” because they like the beachfront say, or even start off well but then compromise their standards to impress balabatim, then the achrayus is on their shoulders.
Or maybe even then it’s on the Rebbe’s as their kids may turn out better than they would have in the ffb community.
Point being, if you are a shliach as in shlucho shel Adam kmoso of the Rebbe, and do your best to lead a life that a chossid should, then the achrayus is on the Rebbe. If you’re not a shliach then there’s no special bracha.