But how does this bigger fear explain why he can't enter without an invitation?
###It doesn't necessarily. The inability for Dracula to enter a home uninvited is a superstition that he falsely believed in just like all the other superstitions.
It doesn't necessarily. The inability for Dracula to enter a home uninvited is a superstition that he falsely believed in just like all the other superstitions.
Numerous times throughout the first season both Agatha and Dr. Zoe Van Helsing pick fun at Dracula for not being able to control his desires, for being a complete slave to immediate gratification/instincts (like a beast). First with Agatha's blood at the gates of the nunnery in S01E01, then with Dracula feeding on all the passengers so quickly in S01E02, and then again in S01E03 when Zoe and Dracula are at Dracula's penthouse talking about Lucy.
A beast [dog] enters a home only when invited, and if the beast attempts to enter unwelcomed then it's subject to being disciplined. The fears/superstitions that Dr. Zoe Van Helsing mentioned at the end of S01E03 were described as, "The Rules of the Beast", and for hundreds of years Dracula blindly followed them all. It was only after Dr. Zoe confronted him about it (by pulling the curtains down and showing him otherwise) that he was able to realize the truth, overcome the superstitions, and then face his fears / death (i.e., become something more than just a beast).
That's how it ties in with everything.
P.S. "The Rules of the Beast" is also the title of the first episode.