My 15 month old is the same way! I bought her a water table for the summer and she spends most of her time standing next to it drinking out of the pitcher that came with it - she also does this in our pool and the bathtub! The pool concerns me because of the chlorine, obviously, but it's almost impossible to stop it. Like you, I started keeping a sippy cup full of water next to her but she doesn't want it. I think it's just how she plays right now - she's fascinated by the water. The only thing I did differently was remove her from the swim vest and put her in a mesh float so she can't get to the water with her face, but you can imagine that she isn't as thrilled with the float as she is with the vest.
Not much advice for you, but just so you know we're going through the same thing. The good thing is, your daughter isn't freaked about her face being in the water so that is great for her learning to swim!