Relation between Livecasino and Bitcasino: Yes. We are the younger sister (brand) of Bitcasino. Our main difference is that we are more focused on Live Games.
Nice finally you have some answers.
Since you are on the same brand with "Bitcasino", I think would be nice (Bitcasino) to make some article posts, something like ANN, or link information for casino under his brand. That's will make more reputation for the casino under his brand (Since BITCASNO really quite popular) + people is not really to worried while there has some similar theme or word with them.