If someone's worried of being snooped by FBI or similar agencies - then don't use Gmail, Yahoo, Microsoft, or any other US company.. And in lite of recent findings - also don't use any UK server or webmail or web site who's data is going over the pan-continental optic fibers, towards US.
The rest of it, like - having your own custom made chat application, that's used by you in one room and your kids in the other, over your own local server machine, provided that the whole thing is off the main grid - is safe!
I'm kind of kidding, but as we learned in past month - that's not a joke material anymore.