There are 4 types of Royal family,they are the same characters but with different actions when you press "c".I only know how to get one of them,marry Prince Tamahiko with Princess Tamako.
4 types of royal family? i believe there is only 1 type of royal family what you're talking about are the bonding animations: as you train your tama family more their bonding goes up, thus when you press C you get different animations. there are 5 in total. but thank you for letting us know about who to marry.