The closest things that come to this in accepted science is known as 'epigenetics' and 'paramutation'.
The DNA in most of the cells in an adult body is mostly turned off. This is done by the cells themselves during tissue differentiation and helps prevent, for example, your brain cells from producing stomach acid. Long-term chemical changes to gene activity levels are known as epigenetics. Some of these changes have been demonstrated to last through many generations.
Paramutation is similar... genes are often turning each other on and off, as in the epigenetic changes above. Some genes have been found, however, that permanently alter other genes - they give you a new, permanent genetic code.
And of course, retroviruses regularly change the DNA of a host as well as more mundane mutations of any sort. Your lifestyle certainly has an affect on how many of these you are exposed to, though few affect you so universally.
There are also conceivable non-genetic traits that can be handed down too, though the mechanism is sometimes less direct. Children get all the mitochondrion from the mothers, for example, and may well be exposed to toxins as well as nutrients while nursing or in the womb.
Some of the known paramutations and longer-term epigenetic changes do occur in response to environmental stimuli. I believe there's a corn gene that permanently makes its heirs more resistant to cold if the plant itself gets too cold. But these things are the small minority - there really are very few things that cause a specific and related change in your heirs, even if we know many ways in which they MIGHT do so.