Only by the strictest formal British business standards is '
Sincerely yours' used with '
Dear Mr Jones' while '
Yours faithfully' is used with '
Dear Sir'. This fine point can be gaily ignored in a casual note such as you are creating-- and after all,
Mom is her name, isn't it?
Actually, in your letter from child to mother, even '
Sincerely yours' sounds overly formal-- why not just '
Love'? And if you do not have the time available to write an individual name on each, '
Your child' sounds just fine. With a little extra photocopying, you could sign half of them '
Your son' and the other half '
Your daughter'-- or you could leave blank spaces and have the kids fill them in in their own handwriting: '
Dear _______ ...
Love, _________ '.