... and note that "welcome to my 'house'" is not natural.
May I very respectfully ask why welcome to my "house" isn't natural to you?"Welcome to my family" does not mean "Hello. My family greets you". It means "Now you are part of my family -- welcome!"
So sentence A happens rarely: it can only be said when a new person "becomes part of" your family, which happens once or twice in a lifetime.
Sentence B happens often: it can be used any time someone enters your home.