Кровинушка - derived from the word КРОВЬ (BLOOD) means someone who have your blood in them in other words - your child. This word is really strong and used rarely. Also can be used to describe someone you like, trust and who's your friend. Another meaning is a small drop of blood

By the way the usual form of the word is КРОВИНКА and КРОВИНУШКА is just the more emphatic way to say КРОВИНКА

As for the soap opera I haven't even heard about it before you mentioned it