Hi @fka,
My first recommendation would be to decide which course will be your primary course and always make changes in that course shell first. Switching back and forth between which one you use will be a challenge.
From there, I would recommend using modules to group your content together (whether it be chapters, units, topics, days, or weeks).
What you can do then is export the course to a downloadable file. You can do this multiple times throughout the semester.
Throughout the semester BE VERY CAREFUL but you can (1) import that downloadable file, (2) use the "Select specific content" option, and (3) pick the specific module(s) that you want to import. The reason you need to be very careful is because (1) you could have duplicates and (2) you could overwrite existing content that you did not intend of being overwritten.
Ideally, and I know that this is not typically the case, it is best to design the course before the semester begins so that the number of changes that need to be made (regardless of the number of sections or number of institutions) is as little as possible; especially when teaching at different institutions.
I hope this helps!
-Doug