Thats kinda confusing, since in NL you actually get letters from your Dad, ans well as your Mom.
If your kids play the game and get a letter like that, they'll think its from you
Well, I was older than average when I first played Animal Crossing, so I probably would never think like that, because at that age, I realise it's just a game.
Apart from a few, I'd hope that most others know that it's just a game and not from your real life parents.