What is the relation between Strike The Blood and Strike The Blood EX? I have read that in Strike The Blood EX, Kojou seems to have two children, so EX has to be set in the future. 

Is it the future of the "world" the story takes place or is it the "future" shown at the end of the anime where Reina came from (you can see Kojou's daughters Reina and Moegi)? Or is EX maybe only the name of the last arc in the anime (where Reina appears)?
Well, during the last episode of the anime (episode 24), a girl suddenly appeared out of nowhere. She looked exactly like Yuukina (but her busts were larger) and she had eyes like Kojou and was a vampire. It is later revealed that she is Reina Akatsuki, daughter of them, and she had come in past (time travelled) to kill a dangerous human-made dragon...
When she got back in her time, it is revealed that Kojou has another daughter named Moegi, but from Asagi..

This is whole is called Strike the Blood EX, I guess