Between with dates with time won't work regardless of whether you use a date picker or not. I think you should determine whether they contain time or not. Either copy your table and play with the copy, or in the current table, go in to design view and format the date field so that it shows time. If you get something other than 00:00:00 then you are storing time. To use a date picker, you'll have to train users to pick the next day after the one they want. Or you're going to have to use a function in an expression to either add the next day from the day chosen, or add enough hours or minutes to the chosen day to include records up to midnight. That depends on what you want. When I had to deal with this, I added up to one second before midnight of the next day because it was a 24 hour operation and didn't want anything after that.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.