Your date picker looks like it's just not including Saturdays in general, which is... odd.
For avoiding the date range issue, the closest you might be able to get is to use a Group Filter, which can act on multiple fields using a single input. Unfortunately, you can only specify a single operator per group, so you would need a single group for the beginning date of the range, and a second for the end date.
Now, that wouldn't be a problem, except that the widget only shows a single group at a time...
So, less typing of dates, but more clicking. Maybe worse than the current situation, since you can't see both dates at once.
A Slightly Different Idea
What if instead of having the date range on both fields, you simply filtered start date as "on or after" and end date as "on or before" and set the filter expression to "match all of the following expressions". Assuming that the value in the end date is always after the before date, such a filter ought to work as intended. By adjusting the filter label text, it can still look like a range, too.
- Josh Carlson
Kendall County GIS