Prayer comes in many forms. What the kids are doing is somewhere between a prayer of thanksgiving and a prayer of supplication. What mom is doing is a prayer of reparation. It’s a catholic tradition in which one not only prayers for the forgiveness of the sins of others. This of course permeates most of the Christian sects.
The kids, since they have no concept of this, are little more than parrots in terms of their prayers. They have no understanding of what they are doing. All that they have a concept of is the ‘grandma told us we have to do this before we eat’
The act of asking for prayers from other people, even if you’re not religious is a social convention.  It’s a similar fashion to saying god bless you when someone sneezes. Do you honestly believe that you will lose your soul if someone doesn’t say it for you? Not likely. However this social convention also carries with it the added notion of thinking about the person. In a more modern context you’re hoping people will take notice and possibly take some kind of action. This is what mom is doing.
This next part is speculator.  The reasoning behind telling the kids that ‘prayer is nonsense’ is the fear not that the kids will be brought up Christian. But rather the type of Christian that would hate those that aren’t Christian. Since neither you nor Nick have ever struck me as the devote type, it would be safe to assume that this influence comes from Nick’s mother. Of the limited evidence I’ve personally witnessed, mom’s fear seems rational in it’s construction.