Edwin isn't even Karen's tutor, is he? She meets him at a party, or something, from what I recall? Of course, he couldn't have been her tutor, or they'd be no reason for the Dodds to relocate to Trennels because of Edwin's archive job -- they'd just have all stayed in Oxford, even if Karen dropped out, and there'd be no story. I think bookworm is right, and AF just wanted to write about a step family, and thus introduced one into the Marlow world. Like she wanted to write a Shakespeare novel, and also put that into the ancestral Marlow world.,
Maybe it helps us to understand why the Dodd storyline feels slightly bolted on to the Marlow world via Karen's slightly unconvincing love affair -- that it's an 'issue novel' featuring the same characters we know from school stories/holiday 'adventure' novels? We don't generally notice because AF is such a good writer, but you could say the same for The Thuggery Affair, and Run Away Home.
I think it just bothers me that clever, ambitious Karen's post-marriage life just seems so joyless. Not only does she is she a housewife with an at best tentative relationship with her stepchildren, her marriage doesn't seem wildly happy, but her relationship with Rowan, the only sibling who is nearby, is distant, and even Giles, unexpectedly home for Christmas, only pays a duty call to check out the new BIL.