Unfortunately not having a stable or strong connection results in a negative impact on the game for other players, and as a result any restrictions or bans handed out for it are completely justified and reasonable. Also when you bought your kids the game they or you had to accept this little agreement at the front in which Bungie said they have the right to ban you at any time and without reason given. They told you right out this was something that could happen and someone on your end agreed. Doesn't matter if you complain or not about it, but the only way to resolve this sort of thing is to get a better or at least more stable internet. Yes, this isn't an option for everyone and it doesn't seem to be for you either, but that's the way it is. Also very mature of you at the end there. Have a good one.