Assemble this in the area needing mopped:
Wait for, and allow plenty of this:
Incidentally, if you follow it up with a lazy mopping job, or delay it a while (since your other young one is sleeping and can't make a worse mess), it also becomes "How To Need A New Floor."
It's either 700 square feet of quality sheet vinyl, installed, or a cheap area rug. I'm thinking the budget prefers the latter...