Do not call it babysitting when the responsibility already belongs to you.

Language quietly assigns ownership. Calling time with your own children a favor, or help, or covering, puts one parent in charge by default and makes the other a visitor doing a good turn. The hours are the same either way; what changes is who is understood to be responsible when nobody is watching. Small words do this work steadily.

Listen for the words you use about your own household duties this week. Say you are looking after your children rather than helping out. Then check that the language matches the arrangement, because the words are easier to change than the habit underneath them.