The strongest influence a mother has on her chicks, or whatever chicks she raises, is in terms of physical health by giving them a good start to life, and psychological health by giving them social experience and tuition. This is very beneficial for their future social cohesion, though family line traits can still trump that early learning and render them socially malignant.
Whether they will go broody or not, mother well or not, is arbitrary... It's by far more genetically based than experience based. I've had monster chick-killer hens bred and reared by great mothers, and great mothers bred by crappy mothers or even nasty ones. You can breed a clutch from a great mother and a great father and still get some non-mothers, or poor mothers, among them.
We've bred maternal instincts and normal familial instincts out of some lines/breeds, many in fact, by using artificial reproductive means for too many generations and keeping them segregated from the natural social group, being the mother, father and chicks family unit. It takes about 7 generations to breed a trait out or in, give or take.
Even if you start off with non-maternal hens, giving them the environment to try if they're so inclined, can eventually render fruit. By this conducive 'environment' I mean having at least one male around, either free range or sufficient room to brood and rear clutches in peace, etc. I do not, however, recommend letting nasty or negligent mothers keep doing half-witted jobs of mothering costing the lives of chicks.
But that's personal choice. I don't give a bad mother a second chance, but some do, and some few hens will learn to mother after a few tries. I just can't tolerate a hen destroying chicks whether it's accidentally or deliberately. A good mother will very rarely cost you a single chick no matter what, whether it's by accident or predator attack or illness... Provided you take reasonable care of them, and their genetics are reasonable so there's no fatal faults for example, chick mortality can be zero. It almost always is for me, and I don't wrap them in cotton wool or keep them in Alcatraz, lol.
Best wishes.