In reverse order, "Please give our love to your family" means, roughly, "please tell your family that I am thinking of them with affection."
It's a rather ordinary thing to say - it doesn't have the excitement, surprise, anger, horror, or extreme happiness that would merit an exclamation mark.
Congratulations to your mother on her Nobel prize! Now that would merit an exclamation mark.
However, I think the writer used these extra exclamation marks to convey the enthusiasm he or she felt; not being able to show with his or her voice her strong affection, etc., exclamation marks were used instead. I use too many of them in my e-mail to my friends as well.