Well the pet civ building nukes should not be a problem... I usually do 3 things to prevent that:
1. Make sure that the pet civ is a 2nd-generation civ, so usually they have just appeared and have no tech.
2. Conquer the world quickly, usually before 500AD. This way they are not advanced at all. The longer you leave them to themselves, the more advanced they'll be.
3. Siege the city. I first attack the city until it is a 1 then use diplomats to destroy all buildings. Next, I place one units on each square in the city radius so that it can only produce a scrap of food and resources.
On one game, I conquered the world in 200AD and by 1950AD (when the game became unplayable due to escalating bugs... this is civ1 by the way) the civilization had built 2 phalanxes and succesfully discovered only one tech since they had been caged: Monarchy. Needless to say, they weren't much of a threat because I was on future tech 200 or so by this time...
One real problem with this is that if you are democracy or republic the seiging units can cause civil disorder, so it's important to counter with luxuries or hanging gardens/cure for cancer. Of course, Women's Suffrage or Shakespeare's Theatre help a lot more!
And one thing to try if you want to conquer the world earlier:
When you kill a civ, don't finish it off. Instead, make it a pet. Do this to all civs, then wait until a certain year (0AD?). I'm not sure of the exact year, but there is a year in civ1 where it is not possible for 2nd generation civs to spawn. So if you wait out till this time, then as soon as it passes, kill them all, then you will get no 2nd generation civs, cuz they can be a real pain, especially if they are on a far away continent and all you have is triremes.
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