It's a game. In Agatha Christie's stories the first to be suspected is never going to turn out to be the actual perpetrator.
What about Melania? Her parents? Barron? Housecleaning staff?
Sorry for interjecting. I just need to stick in some quotes from Hercule Poirot
“When you look your most innocent is when you are up to something.”
“One can’t argue with a point of view.”
“Family strength is a marvellous thing.”
"The truth, however ugly in itself, is always curious and beautiful to seekers after it."