I'm by no means a veteran but I have played a very similar campaign to you. You aren't quite using the cavalry right. If you double click on a target, they will run to chargin range then charge, however the act of them running there will get them out of line and the charge may not even occur. Cavalry charges are, and were, fairly complex things. By all means run to the battle zone, but you must then stop and allow the cavalry to form up. One click to attack will set them in motion towards the target and when they are at charging range they will do so automatically. I discovered this late on in my game and it certainly does help to have a little patience with them.

I found that the only priests I could get increased Piety on were those I sent to the Muslim lands, and those who had vanquished heretics.