Is it permissible for me to leave my parents' house and move to a city 25 km away from them due to continuous problems and their mistrust of me and my wife, while still wishing to maintain ties with them and honor them?

There is no objection to a man having a separate home from his father, and it is the wife's right to have a separate home. It is preferable that the rented home be in the same city as the parents to facilitate their care and righteousness, unless there is a valid reason to reside in a neighboring city.