There's some research on I think it was stickleback fish where the female's first mate determined the size of the offspring. e.g., female first mates with large male, but actually has offspring with a small male --> offspring are still large anyway, despite containing only the small male's genes, not the large male's. Female first mates with small male, but then reproduces with large male --> offspring are small, despite containing only the large male's genes.
The pathway for this is methylation, which changes the EXPRESSION of genes, but not the genes themselves.
Methylation is heritable, generally across multiple generations. Many things in an animal's environment can trigger it. There's a study on humans, for instance, that if a person become obese, it changes the expression of a number of genes (again through methylation), making it much easier for that person's children and grandchildren to then become obese as well.
There's another one finding that if EITHER parent is a heavy drinker at the time a child is conceived, that child is much more likely to become an alcoholic... again due to methylation of the genes. If both mother and father have been off the sauce for some period of time though (I think like 9 months or a year?) then the kid is much less likely to become alcoholic. I guess the parents' genes methylate back?
But basically with those stickleback fish, somehow that initial mating to the larger/smaller males is changing the expression of the FEMALE'S genes for body size... then when she mates with another male later on, the size genes the offspring receive from the mother are influenced one way or another by that earlier mating that caused methylation in her genes.
Why her first mate causes methylation of her body size genes but her subsequent mates don't reverse that I don't know.
There's also no way to know if anything similar happens in humans. It's possible first matings are causing methylation in human women's genes that subsequent matings don't change or reverse... but if so, there's no way to know currently what gene expressions are being affected, and how large or small the effect is.
If methylation from a woman's first / earlier pairings does occur, then I guess if you're a short guy who wants tall kids, knock up a chick who's first lover was a basketball player! Then you're all set. Kids with your genes... but they're giants
Anyway... I wouldn't worry about this too much personally.
If you're looking for long-term / baby mama material, knowing what her exes were like is pretty important IMO... though more so to know what kind of standards she holds for herself. e.g., if all her priors were trashy guys, that says some pretty bad stuff about her, even if she says she has "grown."
Call me elitist though...!
Chase