Most naturally (and most commonly as well), "two kingdoms" would be 「ふたつの王国{おうこく}」.

https://search.yahoo.co.jp/search?p=%E2%80%9D%E3%81%B5%E3%81%9F%E3%81%A4%E3%81%AE%E7%8E%8B%E5%9B%BD%E2%80%9D&aq=-1&oq=&ai=QPWVqZKpRJqYDQmeiYt90A&ts=18497&ei=UTF-8&fr=top_ga1_sa&x=wrt

After the actual names of the two kingdoms have been mentioned, however, you can safely use 「両王国{りょうおうこく}」. It would be highly unnatural and awkward to keep repeating 「ふたつの王国」.

(You cannot use 「両 + Noun」 before both have been identified. You can use 「ふたつの王国」 anytime.)

Most naturally (and most commonly as well), "two kingdoms" would be 「ふたつの王国{おうこく}」.

After the actual names of the two kingdoms have been mentioned, however, you can safely use 「両王国{りょうおうこく}」. It would be highly unnatural and awkward to keep repeating 「ふたつの王国」.

(You cannot use 「両 + Noun」 before both have been identified. You can use 「ふたつの王国」 anytime.)