For the most difficult provinces, honestly, is scrolls and dust provinces.
The reason that it is difficult is quite simple: the three classes of units are all ranged.
The scrolls province features abbot(MA), ranger(LR), mist walker (LR), and orc deserter(HR). It seems to be quite easy for beginner players, as they can use all light melee units to win with thee absence of the orc deserter. But after chapter 3, most scrolls provinces that you found you will meet the orc deserter, which is devastating against light melees. So with abbots that deal the most damage to heavy ranged units, mist walker and rangers that wipe off mages, and orc deserter that take down light melees with ease, it is almost impossible to defeat them using the auto battle mode, unless you have a very big squadsize advantage against them. Using light ranged and heavy melee is not good either, as the enemy light ranged all have strike back and higher initiative, and the heavy melees were seem to slow to take down those units. So if you really want you shall gather enough scrolls and steel to buy this provinces, or you can battle them when you have an overwhelming squadsize.
The dust province features two mages, the abbot and banshee, light ranged wild archer and heavy ranged steinling. Unlike the scrolls province, for chap 1 and chap 2 players it's the three types of units except the wild archer. So you know how difficult it is—— you have no choice but still need to conquer it. The first mage unit (for elves, sorceresses, for humans i don't know bcuz i never play with humans) is unlocked at chap 3, but in chap 3 dust provinces have wild archers to take down your mages so you must be very careful using them. Like the scrolls province, using auto battle with a same squadsize is almost impossible to win (with all three classes of those units present) so using autobattle is strongly discouraged for this and perhaps you will still have to seek for negotiation if you like to advance quickly.
And for the tournament, the same problem happens as well. I think the first three rounds will be a little tricky to complete, but how about the last three rounds? The enemy will usually have an even overwhelming squadsize against you, and the catering costs is also very high, too, requiring hundreds or even over 1,000 goods to cater. So, i believe that negotiating is the best choice to conquer these provinces in later ages instead of fighting them. If you still want to fight them, train a lot of light melee units, use them to kill the light ranged and mage units, and after they were killed, use heavy melee units to finish the rest of the heavy ranged units, though if you really do so you will have to suffer a lot more sacrifisation than encountering any other provinces (i don't know if this works for you) ! If you have the steel+scrolls+dust production boost, it's even better, you will be able to deal it much easier than fighting!
In conclusion, provinces is pretty problematic with all units ranged