Vatler had proclaimed a few times that he was in love with the previous Fourth Primogenitor, more precisely the 12th familiar's master, Avrora Florestina. However, the exact nature of the feeling or the full extent of it has not been explored further, leaving the proclamation somewhat lose a lot of its credibility.
He became interested in Kojou after Avrora's death, due to Kojou inheriting her blood and all of the power that resides in it. As the story progresses, it's become apparent that he somewhat has some degree of obsession towards Kojou, be it in regards to his vampire power or towards his development and interactions with the girls.
He proclaimed Yukina as his 'love rival' in their very first meeting, seemingly assuming at that time both of them as active competitors for Kojou's affection.
She was briefly in charge of observing Dimitrie Vatler. Vatler most likely thought not that much of her, aside from a slight interest due to her relationship with Kojou.
Looking at Natsuki's apparent disdain in regards to Vatler, it's almost certain that they had had some not-so-friendly encounters in the past. Though, as far as the current story goes Vatler is more amused at her power, not showing any signs of overt disdain like Natsuki always does.
As people with high authority from their respective nations, both Vatler and La Folia had been shown interacting in official capacity at least two times in the light novel: the first was when La Folia was about to leave Itogami Island after the Angel Faux incident; and the other was when La Folia went to Japanese mainland to investigate the Knights of Cleansing. In both of those interactions, they seemed amicable enough to each other, though not showing any special kind of familiarity or comfort either.