Guideline #1 – Don’t suggest, while getting ready to leave the house for work, to one of the children that “Maybe you and Mommy/Daddy could do xyz today.” The child will not hear the “maybe” part and will instead hear, “Mommy/Daddy and you will do xyz today.” It is understandable that as the parent leaving the house to go to work that, if you were home, the aforementioned activity would be something you would want to do with the children. It’s probably best that you keep that thought to yourself (or perhaps run it by the parent staying home first) and save it for a day when you will be home.
Otherwise, the parent that’s left behind will spend the rest of the day explaining to the child(ren) that you will not be doing that activity today even though their other parent for all intents and purposes said they would. You never know what the stay-at-home parent may have planned for the day nor why they may value, say, cleaning the house over the activity you suggested. :0)
For the record, the converse is also true.