If you're wanting to keep water and milk separate in terms of what you give it to her in how about getting a sippy cup or a straw cup which is only for milk? DS has his water in his straw cup and when ever we give him something different, either water with fresh lemon in it or fresh home made juice or sometimes oat milk we give it to him in a regular glass that we drink from (which we hold) with a regular straw (that ds holds in the drink). That way he knows that his water cup which he has free access to all day is just for water and any other drinks are special and we give them to him kwim. I know your dd is younger but the point is that if you make it clear that there is one special cup for milk and the water cup id separate.