@Robin1 I have two listings as well, one for the entire apartment and one for just a private room. First, you're doing the right thing by not having "instant book" activated. (You could have for one, but definitely don't do it for both.)
Second, you need to be vigilant. If you accept a reservation on one, immediately jump over and block out your calendar on another. Airbnb doesn't automatically do this for you.
Third, if you haven't yet discovered it, check out the multi-calendar view. You can either try this link or follow the desktop route here:
This has been enormously helpful in making sure I don't accidentally double book.
--
If my answer helped you, please give me feedback on my listing! https://www.airbnb.co.uk/rooms/9285982