The amount of information transmitted from one generation to the next is potentially much more than the contents of DNA. DNA is not an encoding of every detail of a living body, it is a set of instructions for a living body to create an approximate copy of itself. You can't use DNA, as far as we know, to create a new organism from scratch to create a new organism without having the parent organism around to build it. We do know for certain that many parts of a cell divide separately from the nucleus and have no relation to the DNA of the cell - most well known being the mitochondria, which have their own DNA, but also many organelles just split off and migrate to the new cell quasi-independently. And this is just the simplest layer in some of the simplest organisms - we have no idea whatsoever how much other information is transmitted from the parent organism to the child in ways other than DNA.

In particular in mammals, we have no idea how actively the mother's body helps shape the child. Of course, there's no direct neuron to neuron contact, but that doesn't mean that the mother's body can't contribute to aspects of even the fetal brain development in other ways.