I too was bored to tears by the Captain's family soap opera. That's not the kind of scene I watch this show for.
Normally I hate that stuff, too. But this was providing some background for him and gave some extra info. He’s not one of the witnesses; he can step away from this. His talk with the priest(?) gave info that he’s a man of faith, or was. And the fact that he’s willing to continue with Ichabod/Abby shows his strength of character. His errors in his marriage shows that he’s flawed, but is willing to continue despite his flaws. His apology to his ex shows that he’s realized and accepted responsibility for his mistakes, isn’t blaming her, and actually sounded like a goodbye, in a way.
The scene with the priest also counterposed the scene with the possessed hot chocolate vendor. It also showed that the “evil” is aware of him. And his daughter. You can tell there’s going to be a choice: fight evil or protect daughter.
Unless his daughter takes a prominent role (which I think she will, but hopefully not too much), this was sufficient to round out his background.
I do like him with Abby’s sister; the characters interact well and there’s enough chemistry between them.
I noticed that Ichabod is the only white main character. I like how that was done without making a big show of it. Well, now John Noble is recurring, and the sister is more recurring than main.