Thank you for your review on Miscellany, and apologies that it's taken me so long to reply.
What would happen next is that Sesshoumaru would start taking more interest in Rin's education, and would start to regularly attend parent-teacher meetings. Rin would continue to find excuses and situations by which to make Sesshoumaru and Kagome see one another, and would have full support from her grandmother.
Nothing much would happen romance wise, though, until Rin would graduate primary school and move on to secondary school - since asking your daughter's teacher out on a date wouldn't be quite proper, and Sesshoumaru - despite his faults - is a gentleman.
Thank-you for the review on A Miko's Peace. I try to update at least once a week. One rare occasions I'll update twice a week. It really depends on how I'm feeling that week or if I've been inspired to write or not. I hope to keep you as a regular reader though and I hope you continue to enjoy my story.