Where are you located? If it is somplace humid, it may be impossible to get all the water out from inbetween the walls and you could end up with mold/mildew.
Your fittings are obviously not tight enough and not sealing properly. What are you using for your drain valve? As far as draining it, your best bet would be to drill some drain holes just through the outer layer, on the bottom of the cooler. Maybe a half dozen or so 3/16 holes would allow it to drain.
Good luck with it!