That's what I was afraid of.  It seems chickens need a little more room, but can stay confined more.  Ducks can have smaller houses/coops but need a lot more space.  I was just hoping having a small number would work for me.  The closest tree is three houses away, so there's no shade at all.  The only shade would be the roofer over the coop/run. 
 
It looks like I either have to fix the sogginess to house chickens, or figure out a way to fence off the dogs to give the ducks half the yard.  Are you saying that I could have the run/coop and leave them out with 3.5 to 4 foot tall fences on each side?  I have only seen hawks flying in the neighborhood a few times.  In the past 18 years, I've seen one opossum, zero snakes and 3 mice and a few hawks.
 
I appreciate everyone's help.