The thing that came to mind for me: habits if mind are tough to change. Both Sesshomaru and Kagome have some habits to change.
Sesshomaru has already decided on his, but he's probably got a lot to sort through in his mind and heart as he works through his centuries old habits and attitudes. Right now he seems to be in that nice euphoria-like state that accompanies new resolutions; how long will that last before he backslides? Will it be a large or small backslide? Probably both - and more than once while he forms new habits. No one is perfect, not even Sesshomaru (though we like him to be
) What will the consequences of his backslides be?
Kagome still hasn't figured hers out yet, but actively realizing that Inuyasha doesn't love her the way she wants and needs (and he never will) and then learning to let to of him will be a tough adjustment too. No one wants to admit that they've wasted their time in a futile endeavour; generally people prefer to persist in their behaviour rather than admit that it was futile and change. She could come to this realization a little more gradually than Sesshomaru came to his, but it's got to happen for any other romantic relationship to follow. Even then, she's likely to follow some of her habits for a while afterward. What will the consequences of that be on her relationship with Sesshomaru (either friendship or romantic)?
Frustration, anger, confusion, and misunderstanding will probably abound between them; they've got such different mindsets and grew up in vastly different circumstances, so how could they not? But there is so much potential for them both to grow into stronger, more flexible, more resilient people!
Unless you're looking for a really unique outside-the-relationship plot, it seems to me that the character changes could be enough to keep things driven. Habits are best formed through our everyday lives, and their everyday life right now is hunting shards and Naraku. Will the Inutachi run into more or less crazy with Sesshomaru hanging around with them...? After this point, the story wouldn't even need to be a day by day account. Changes take time, so we could drop in on the group every few weeks or months to see how things are going...
Hope something in that set of thoughts helps!