Whole grain flours are healthier than white flours. So you want to change them, but you don't want to do that overnight as that will cause revolt. Therefore you're better off changing that gradually. In small steps. You also want to make sure that you treat your grains well before consumption, so that they are nutrient dense.
The way to go is to first change your white flour yeast bread into white flour sourdough bread. That way your family will get used to the sourdough flavour before you bombard them with even more flavours. Whole grains are full of flavour, so you want to take it slow.
Once your family is used to the flavour of sourdough, which will be a bit more acidic than yeast bread you can take the next step. Introduce whole grain wheat flour. That isn't a huge difference in taste, so it shouldn't be the hardest. After that try spelt whole meal flour, then kamut, that tastes a bit nutty. Rye adds an acidic type of flavour as it's a bit sour.
Once the fam is sorted on the whole grain bread flavour try some other things. Soak your oats in an acidic medium, some prefer a bit of apple cider vinegar, others prefer lemon juice and even orange juice can be done, as long as it's a bit acidic so the phytic acid gets neutralised. From there on take more steps, one by one, and take your time.