@BoraMac Think of "kita" as an "abbreviation" of "ko ikaw."
Niyakap kita.
Niyakap ko ikaw.
I hugged you.
Uuwi kita.
Uuwi ko ikaw.
I'll bring you home.
Generally, anything that can be said as "ko ikaw" can also be (and preferably) said as "kita," and vice versa.
Hmmm, it is actually strange how "combo pronouns" don't apply to UM verbs.. "Yumakap ko ikaw" or even "Yumakap siya niya" makes no sense to me..
I guess the rule would go something like: "Pronoun combinations, that is the ANG case and NG case are both pronouns, only agree with IN verbs (including locative, instrumental, anything with the IN affix)."
Another thing I noticed, the NG pronoun always precedes the ANG pronoun in a pronoun combination - "Mahal ikaw ko" makes no sense either.
Kita is the only "proper" "abbreviation" of a pronoun combination in Tagalog. But interestingly enough, in Kapampangan - another language here in the Philippines - most pronoun combinations morph into a different word:
ku + ya (tagalog, ko + siya) morphs into ke,
mu + ya (mo + siya) -> me,
ku + ika (ko + ikaw) -> da ka,
mu + yaku (mo + ako) -> mu ku.
(taken from Wikipedia)
EDIT: contraction -> abbreviation