Is it permissible for a wife to travel to visit her family without a mahram, and without there being marital disputes, merely for the sake of showing affection to them, and what is the permissible duration for that, and what are the rights of each spouse over the other?

There is no blame upon a woman for seeking her husband's permission to visit her relatives and stay with them for days, as long as the visit does not involve anything prohibited by Sharia. Both spouses must live together righteously, with understanding and compassion. Part of beautiful companionship is for each to be kind to the other's family and to help them honor their parents and maintain ties of kinship.