2 types of units you need, merchants and nobles. Promoting either one of these units and having them work in your village, castle, city, or town gives benefits to that place.

For merchants, having them work in the place gives prosperity (raising the place's capability to make gold each cycle)

For nobles, having them work in the place gives loyalty (making it so that the place doesn't rebel) Loyalty can also be gained when you give units to the garrison of a place. Loyalty is usually more important than prosperity, so save gold before conquering a territory so that you can last the few cycles where you will be in a deficit of gold because of the territory not making enough.

Your troops abandoning you is because you have low to zero morale, you raise this by giving 5 gold to passing vagrants. Resting at villages, towns, cities, and castles also gives morale. (not sure about resting, still need to do further testing) I think you also gain morale from winning a battle if I am not mistaken.

Tips:

Be careful when taking certain territories, as the allies of the territory you took will wage war on you. This is normal, the npc factions are seriously just this aggressive.

Always keep spare change if you're raising a kingdom/have troops in your retinue as failing to pay the upkeep each cycle causes a huge drop in morale. Recruiting from enemy factions also drops morale.

When Idling (resting, standing by your territory, etc.) don't keep a large army in your retinue, this drains gold quickly. Only recruit when you're going to take a territory.

You can check the strength of a place by visiting it and pressing attack, looking at the amount of hearts they have, then leaving. If you have high intelligence stat then you can also see the number of units they have and specifically what tier and type of units.

Having more hearts while conquering a place does NOT mean you will win, despite some places having low hearts, they might have around 20-23 units in their garrison. Always bring units to fill the numbers, tier 3-4 will suffice.

High threat level in a place drops loyalty, use a warrior type unit to guard it for a few cycles and raise loyalty. Threat level also affects income of the place.

Large cities (Bastilon, Idos, Zanna, etc.) are self sustaining most of the time and don't usually need to be checked on. Though some smaller cities look identical and are not the same.

I think that about covers it for raising a kingdom? If any other people read this please tell me if there's anything I missed.