Translation:This favorite child is the youngest.
I gained the impression that "põki'i" is specifically referring to the youngest child in a family/set of siblings, while "muli loa" just literally means "very young" or "youngest".
I assume that "muli" can be translated as "young" in general, while "põki'i" is restricted to that context of a family. Perhaps we can find examples of the word "muli" being applied to nouns and items other than siblings (and people!). Aloha!
Equational Sentences, HAW 101
ʻO (Slide 8 to 14)
(Grammar Link): https://www.slideshare.net/malama777/aike-101
muli loa = youngest
muliloa [muli·loa] n. last born child. (NKE)
Same thing. Imagine being a translator for a government official in negotiations. You don't have the option of summarizing the gist - the speaker chooses the specific words for a reason. Pretending like this helps me stay true to the structure, even tho the meaning might be stated in several similar ways.