Every now and then you come across with strong kingdom who is standing right in your way, and with so much soldiers that military action is either impossible or punitively expensive.
This is when you shall use the unstable nature of large kingdoms against them. If you have ever had moderately large kingdom to rule and your ruler died, you must know how easily things start to get difficult. Same is true for AI...
Which is how you shall defeat enemy you could not conventionally defeat. It requires at least few things which are:
1. Enough gold to assassinate at least two people
2. Enemy with preferably agnatic-cognatic primogeniture/gavelkind succession, underage female heir near top of the list is excellent bonus.
Preparations require placing spymaster to build spy network in the enemy capital and, if necessary, chancellor fabricating claims for strategic locations in enemy realm (or getting any other casus belli you may get). Preferably using other means but holy war, as this way you do reduce risk of having their brothers in faith from interfering.
In most cases, strong kingdoms will have strong ruler who has aged already but might have decade or two of fight left in him, along with adult heir who has gained some spurs and is growing to fill his fathers boots. By assassinating father, you can weaken the kingdom, but if heir is sufficiently strong already, he can keep it mostly together. That is why you begin to murder your way until you reach their children, who at this point are woefully underaged and preferably female. Or whomever is the weakest link.
Short reign, most likely regent who is not up to fill the boots of old ruler and possibly female ensures that in short while the realm is fighting against itself, wasting armies. Now is time to start looking at their territories more carefully and preparing your army, that is if you want to make sure they stay down. Let your opponent kill each other for a while, waiting until they start to occupy territories of one another. It is important to keep tabs on who is winning and who is losing, because prolonging this war is going to be in your interests. Always hit one who is on top, declaring war and snatching some of their territories away from them.
Because you fight both sides, you can attack them in turns, leading to situation where every 5 years you can attack one or another while still respecting the truce with other.