Currently, the textbook issue has developed into an important problem spanning both countries, between the governments of Korea and Japan.
Literal
Currently, Korea [and-と] Japan [attributive-の] governments [between-との間で], textbook problem [subject-が] both-countries-between [to-にかかわる] important problem [to-へと] is-developing-[continuous-ています].
International relations news. ~との間で ('between X and Y') marks the space between parties. ~にかかわる ('concerning, involving, spanning') is the attributive form of 関わる. ~へと is the directional particle ~へ + と marking a destination/direction of change. 教科書問題 ('the textbook issue') refers to the long-running dispute over Japanese history textbooks and their treatment of WWII and colonialism.