If they don't have an army (a stack) at their disposal they are less likely to rebel. Even if they do you have an army already in the province to oppose a single unit of rebels.
Low loyalty leaders moving in with the king is not always an option - these leaders may have a high command and may be needed as generals elsewhere, so out-of-stack position is a compromise between a possible rebellion and leaving a province with an 0-valor army.
How do you choose the capital for the king to reside in? I choose a province reasonably far from possible invasions and with the highest level of armorer and metalsmith (if available). In the latter case all princes that come of age will appear in this province with all upgrades the province can give them.
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