The schedule builder handles the common patterns — alternating weeks, 2-2-3, every other weekend — and shows whose day each day is, on the calendar both of you see.
Once it's set, handoffs come from it automatically: you don't have to add every changeover by hand.
When real life differs
Add an exception for the day rather than rebuilding the pattern. The schedule stays the agreed baseline, and the exception is recorded as exactly that — which is far more useful later than a quietly rewritten schedule.