Roads are not owned within enemy territory, so you can still use them, which makes using caravans a very risky proposition. While I understand from a realism standpoint there is nothing stopping that approaching army from using your roads, from a game perspective, it creates much-too-fast approaching armies. Enemies shouldn't be able to use roads if they're in enemy borders. Indeed it would be nice if buildings/tech/magic could reduce enemy movement while within your own borders.
For that matter borders should not automatically flip once you have conquered a city. The enemy should retain their control for a few turns until you quell the rebelious citizens. This should also serve to assist the defenders in retaking their city, since they will gain the territory bonus while doing so.