Is it permissible for a husband to prevent his wife from visiting her sister, and is he obligated to accompany her if he allows her to visit?

It is not permissible for a woman to travel to a distant city unless accompanied by a husband or a mahram (definition), even for the purpose of maintaining kinship ties, according to the majority of scholars. As for her travel to a nearby city, which is not considered travel, there is no harm in her going alone if she is safe. Some scholars permit her travel to maintain kinship ties without a mahram if she is safe.