Could the prayer be used to specify it be applied to one’s family members wherever they go and come in contact with other people, such as going to school, to work, visiting friends, and so on?

Here again, as a divine human you have a birthright to request anything you can think of, of the divine. This is not a guarantee all will be answered, or in the way you like, but what you are asking for here is only something that any soul-based being would wish to have from the divine on behalf of the loved ones. This should be routine and taught from infancy, how to partner with the divine and arrange for divine assistance for all beings, everywhere. This is the ultimate expression through GetWisdom of the idea of saving and healing humanity through healing the perpetrators as well. You are only asking for a smaller slice of the pie in this prayer, but it is good to specify high priority needs, and this you have a right to do as well. It will fuel those prayers with extra intention to make them even more effective. The routine, recommended, daily prayers from Creator will deal with the kinds of issues you are addressing here, with a specific focused prayer. But it is always good to identify needs and provide that specificity to the divine. The squeaky wheel does get the grease, and this, again, is a birthright you enjoy. You are in control of your destiny more than anyone else. This is your domain and you are running it, if only by default, in ignorance, not realizing you are in charge. So when you decide to take charge and ask for something extra, you are well within your province to do so, and this will be honored.