calsmom, there are waterers available for chickens raised on a commercial scale; they are durable and sanitary.
Concerning the rain trough idea, I expect that the liner will bulge through the spaces between the fence staves. The other problem is that of keeping the plastic supported vertically. A pond liner is kept in place by a 'deck' made of decorative heavy material. The possibility exists that the material can be punctured by splinters, nails and the like. The pool liner which I used for an inground decorative pond got punctured after five years of proper care and maintenance. My next effort is going to be a rigid structure (absatively! posolutely!). I've seen a bathtub used in an application similar what you are planning.

I am considering the same scheme but in my humble opinion, your design would not be strong enough. Water is very heavy and when you put a lot of it in one place,it can put a lot of pressure against the structure. How about finding a used above ground swimming pool for kids and use that.

According to my calculations, a small pool 10feet in diameter x 1.5 feet high would hold 881 gallons !! This equal to sixteen 55gallon barrels. These pools are usually available in craigslist or even new are not very expensive. A plastic sheet for a cover would keep mosquitos out.

Tim