How about an option to allow cities to retain their current cultural border when you capture them militarily. Often it doesn't make sense for another country's culture to completely overwhelm your newly taken cities.
And secondly, military units should have the ability to "take over" another civs cultural squares. In war time, this could be used for example to string a line of units together to control a rail line in foreign territory. In peace time, this could be used to take a strategic resource away from a competitor. This would surely impact relations and if the competitor doesn't like it, they are free to declare war of course.
When the UN is built there could be an method for assigning permanent borders that don't change from culture influence or redrawing borders for special situations.
And secondly, military units should have the ability to "take over" another civs cultural squares. In war time, this could be used for example to string a line of units together to control a rail line in foreign territory. In peace time, this could be used to take a strategic resource away from a competitor. This would surely impact relations and if the competitor doesn't like it, they are free to declare war of course.
When the UN is built there could be an method for assigning permanent borders that don't change from culture influence or redrawing borders for special situations.