Hi! I'm new to the boards here but I thought I would chime in as this is very applicable to us.
I work part-time, one day/week up until a few months ago. For the better part of our hs'ing, dh has had his one day per week. On that day he did RAs or a field trip and Karate class. I have just upped my hours to 2 days/week and we are finding that the kids need more on my days. I did a schedule of work that dh (ideally) completes with the kids over the course of his two days, sort of a substitute teacher idea. I use a donnayoung.org form and give them assignments for Math, LA, reading, spelling and readalouds. I still do most of the history and science. This seems to be working well so far and I can see an improvement in the kid's attitudes because there is more stability and continuity to our week.