Sorry to (slightly) correct u Anthonius.
1. the place is called Hattin
2. The armies in the Latin Orient mostly were recruited out of immigrated "soldiers"; not of troops recruite out of the cities in the Holy Land as they where primary muslims.
The Nobility of the first Cruisade who managed to conquer the Holy Land was pretty mutch tolerant against the Muslims, but didn't recruit many troops out of them as they where "heretics" still.
The holy land mainly got their Military strength out of "cruisaders" (including Knights, Peasants and all those folks) and the religiouse military Orders like the Johanites and Templars.
Btw those military Orders were the only one who could support the Kingdom with larg forces of well equipped Soldiers, Sergants and Knights as they didn#t relay on the regular Feudal system.

So mutch for the Correction ;)
The latin Orient was overrun mainly cause of the Unification of the Islamic world by Salahadin, aswell as the lack of new Cruisadertroops to refill the lost troops after the Battles of Hattin and La Forbie.
As holy Wars shifted to more near Locations like Spain and the slavic East, the shifting of traidingrouts and the new ways of policy, no King of europe was that Intrested in gaining Honor in the Holyland anymore ;)

I would try to limit Troopsrecruitment for the Kingdom of Jerusalem to Christian population only ;) (can't say if it is like that in the game- i never tried to conquer that city ^^)

As for the Peasants. You're primary right for the Tradition, as it looks down on the Peasants. But as the Peasants in the early and high Middleage where not equipped by the Lords for battle, but mainly just took what they could get, they where not that important. The Knight as a higly traind and Skilled Warmachine still was the backbone of every Army.
After after the Wars against the Swiss peasant armies (starting 14th century) who introduced new Tactics for Footsoldiers and the battle of Azincourt they way of medieval Warfare slowly shifted to Mercenary Armies