The science overall is very favorable for vegetarian vs omnivorous diets. E.g. "RRs for all cancers were 0.82 (0.73-0.93) in pescetarian and 0.88 (0.81-0.96) in vegetarians". However "vegetarian diets may lead to an inadequate intake of several important nutrients, particularly Fe, Zn, vitamin B12 and n-3 PUFA, which are associated with some disadvantages and health risks" So perhaps don't be strict and perhaps take a supplementary multivitamin containing just a little zinc, iron, B12 and omega-3s.
With all these studies the question is: is this association causal or not? For this review, they found " all-cause mortality in cancer survivors decreases with increasing amounts of exercise". Does the exercise reduce your risk of cancer recurrence? Or are people who are not likely to get cancer recurrence for other reasons, happen to walk more? We don't know but I figure better to put yourself in the lower risk category if you can!
"Contrary to the pharmacological approach of cardiovascular prevention, the adoption of the Mediterranean diet has been associated with a significant reduction in new cancers and overall mortality". If you have high cholesterol, it might be just as important to switch to a Mediterranean-style diet as it is to take medications to lower your cholesterol.
"Physical activity may be as or even more important than pharmacotherapy for reducing the risk of mortality in adults with hypertension. However, the risk of mortality remained higher for physically active adults with treated and controlled hypertension than did the risk of mortality for physically active normotensive populations. Prevention of hypertension is therefore imperative for reducing the all-cause risk of premature mortality in adults. " We have been telling patients to think of physical activity as the most important medication you can take. Take it every day.
More helpful tools for nagging your daughter-in-law: "An infant diet consisting of high levels of fruits, vegetables, and home-prepared foods is associated with less food allergy by the age of 2 years."