I have built an iron farm on a server with four villages but only one of them is spawning golems. For symmetry I use 128 doors in each village and they are all fully populated due to brown coats harvesting potatoes. Now, I know the villages are not merged because the golems are spawning on the platform I set up in the middle of the one village and, if merged, the centre where the golems spawn should have moved. The village spawning the golems is the one I started with and took villagers from to populate the other villages. So, what could be the cause of three valid villages not spawning golems?
If the iron farm is not automatic or not killing enough of the Iron Golems due to entity overloads they may not be spawning because there are to many of the Iron Golems at one time.
You have to have the villages 100 blocks apart, and the population has to be 10 or over, and 21 doors or over. I do not know why, but try the 100 blocks apart bit.