Agree with comment about God setting people up the way they were supposed to be born. However, if God gives up the ability to change that, then might that be God's will, too? For instance, many people are born on the bottom rung of the socio-economic ladder, and yet they could conceivably climb that ladder and end up on the highest rung, with their children being born into that level. Was God's will for those people to stick on the bottom level? Although they were born into that status, obviously not. Already, the epigenome has been altered by scientists methylating parts.
As for intergenerational effects, the article mentions starving Swedish grandfathers affecting their grandchildren's longevity. That's two generations right there. Furthermore, if parent '1' affects the epigenome of child '2' for that child's entire life, then child '3''s epigenome could be affected, too. And then child '4', '5', etc. Suspect that if that is the case, then the affects would weaken with each generation, but still have some affect on the epigenome for generations. A hypothesis to be sure, but not too much of a stretch.
Sounds right but then some good times and a happy family life for Mom might counteract that in the interim. But it does make your long term theory more likely.