JEC; my first instinct when hearing that this little person was tired at the end of the day was to think "I betcha it's MOM that's tired, not little one!" Understandable, but putting the child down for a nap so that she can make supper, take a breather, etc is not going to be helpful in the long run. I would stick to what you feel is best for her (the child). Try some of the above suggestions to help her get a little rest, when needed.
Best of luck!!!