"Help Kaʻiulani clean windows."
Translation:E kōkua iā Kaʻiulani ma ka hoʻomaʻemaʻe puka aniani.
Your second choice should read - E kōkua iā Ka'iulani i ka ho'oma'ema'e i ka puka aniani. You are right, though.
What they are doing in the answer is using the direct objects as adverbs to modify the verbs directly.
Kui au i ka lei. I am stringing lei.
Kui lei au. I am stringing lei.
Oh, I've noticed this. E mālama kālā / E mālama i ke kālā; E ho'olilo kālā / e ho'olilo i ke kālā; E puhi palaoa / E puhi i ka palaoa; E kahi lauoho / E kahi i ka lauoho; etc. But look here: Help Kaʻiulani clean windows. Plural. The meaning is unbroken, but it is a bit different however. So: i nā puka aniani? The most nice answer for me is: E kōkua iā Kaʻiulani e hoʻomaʻemaʻe i nā puka aniani.
As far as I understand, Hawaiian plurals can often be expressed as singulars - when plural is implied, but it is simplified to naming a thing. For example: E holoi i kou lima - wash your hands. Not: E holoi i kou mau lima. The hand is ka lima. Hands are also ka lima. Perhaps, if the hands of several people were meant, then nā or mau would appear. For this reason, in this sentence we write ma/i ka hoʻomaʻemaʻe_puka aniani - no article at all, just naming a thing.
Hawaiian often uses singular when it's understood to be plural. ©