However, I have found that burnout is real, and it can’t always be staved off with sheer willpower.

I have made compromises over the years — including letting the children watch television when I am sick or against-the-wall exhausted — because I have weighed the alternatives. If you have relatives you can trust, by all means call on them. If not, IMO, occasional use of Mr. Rogers as a babysitter is a compromise that will in the long run be beneficial. I tried sitters, and Mr. Rogers is kinder and gentler than the ones I encountered. And he costs less — no small consideration for a single mom.