"Which ball do you want?"
Translation:ʻO ke kinipōpō hea kou makemake?
But that is a different idea being conveyed. The prompt is "which do you want...". Your "makemake 'oe" puts the want/desire at the front of the sentence, rather than the options up front. And your proposed translation actually limits the choices to two, not implied on the prompt. These are 3 very different sentences, conveying related ideas with different emphases. The prompt emphasized "which one?"
ʻO describes an equality between "the ball" and "your desire". Notice there's nothing obvious in the sentence which says "which ball IS your desire?" There's no "is" in Hawaiian. Showing a state of being like this is done in different ways. In this case, ʻO tells you that "which ball" = "your desire"
For example, ʻO wai kou inoa? A common way of asking someone's name, is an equality and can be thought of as "what" = "your name"? Then the reply: ʻO Kalei koʻu inoa Here the equality is that "Kalei" = "my name". Notice that ʻO has two uses here that overlap, since you also need an ʻO before people's names.