Am I entitled to prevent my Muslim wife from visiting her non-Muslim grandmother in another country, and how should I deal with this situation?

The wife's obedience is to her guardian if consummation has not occurred. You should speak with him if you fear corruption for her; otherwise, it is better to avoid discussing her travel. However, if consummation has occurred, it is obligatory for her to obey you, even if she is in her father's house. It is advisable to be deliberate, wise, and to work towards everything that fosters affection.