What we're learning is that epigenetics is a determining factor much more than genetics. Epigenetics is an emerging area of scientific research showing that many health problems are due NOT to "bad genes" but to genes that improperly switch on and off within the cell. We all know what happens when cells go completely haywire - cancer cells for example. But there are many smaller "misfires" that go on within the body, causing a whole host of problems including inflammation, autoimmune issues (MS, lupus, RA, fibromyalgia, and many more), allergies and many mental health issues such as depression and ADD. The damage to the epigenome (which is the covering of the genetic material) is influenced by a variety of factors, including foods, lifestyle choices, disease, and the environment. Research is showing that our food growing techniques (including but not limited to GMOs - genetically modified foods), environmental toxins (what we breathe, touch and ingest), and what is added to or stripped away from our foods during processing have a HUGE effect on how our genes function. Every cell has the same genetic material, but the switching on and off of certain genes is what allows cells to diversify (nerve cells do something very different from skin cells, muscle cells from bone cells, etc.) When they switch on and off improperly, the cell doesn't do what it's supposed to do. Over the past generation, the huge increase in things like food allergies, ADD and autism, plus the conditions I listed above, have to do with the spread of this damage.
The good news is that the epigenome can be repaired and influenced. If you do nothing, I'd say your kids are not so likely to "inherit" these problems from grandpa as they are to develop them because of other factors. However, with the discovery some 16 years ago of a natural peptide that is the first superfood proven to influence gene expression, these problems can be prevented and often reversed after they get started. In my work, I've seen tremendous reductions in ADD/ADHD symptoms/behaviors, for example, as well as the virtual elimination of food allergies (which is the body's abnormal reaction to what should be a harmless item). In my personal life, I've virtually eliminated all disease, haven't been sick for 6 years, and no longer require antidepressants.
So, again, doing nothing will not protect your kids, but they are not the helpless victims of their DNA. Lots of people have conditions now that have nothing to do with a family history, and that includes the mental health issues you list.
You can certainly take a few simple steps to supply the necessary nutritional elements to ward off a whole host of problems and give their bodies and minds the tools to do what the body really wants to do - which is to be whole and healthy and fully functioning.