Also note that it's extremely difficult for new cities (or newly conquered) to push back even the extended borders of old cities, however much culture they produce.
But presumably you will lose the unhappiness penalty for "we yearn to return to our motherland".
Razing and rebuilding doesn't help at all as the revolts are not linked to the population in the cities but to the culture present on the tiles that you just conquered. This culture will remain even after razing the city.
But presumably you will lose the unhappiness penalty for "we yearn to return to our motherland".