Looking at the respective royal websites and social media accounts it seems that Queen Margrethe uses R to sign official documents both domestically and abroad (her grandfather famously signed Christian Rex and caused a diplomatic incident with Hitler because of it), King Carl Gustav uses R to sign official documents aimed at abroad and King Harald at least uses R to sign official documents aimed at abroad (I haven't seen a document signed by him aimed at domestically).
What is the reason for using R internationally and not using it domestically?