Drowning a chicken

This week I found a little wild bird dead in my chicken's water container inside their run. I often see wild birds in there that go in for the food. I don't know what happened to this little guy, it was far too late by the time I found him.
Then tonight I was sitting outside with my chickens and a thought came to me. My dominate hen, Peep, wasn't letting the lowest hen, Frances, get a drink from the dish she (Peep) was drinking out of. Peep chased Frances away pecking at her. Frances then went to the kiddie pool I have in the backyard for the dog and hopped up on the ledge and got a drink out of the pool. But my third chicken went over and I was afraid Frances was going to end up in the kiddie pool. Now it's not that deep, I'm sure her head would be above water if she were on her feet, but that got me to thinking would she panic? Is the dog's kiddie pool a danger to my chickens?
P.S. I have two water dishes for them. One in the run (where the wild bird died) and one in the backyard that Peep was defending. It is not as if Frances can't get to water if she needs/wants to.