If in your game Northumbria is at war with Alban too, I would suggest hitting them first, even ignoring the losses from welsh kingdoms. They are light armored and weak in sieges, you can take whole of scotland in couple weeks with army of 200-300 men. Even their capital which had over 600 troops wasn't too problematic. Part of your army needs to be elites, the tavern bought are enough. If you can't afford them yet, there is nothing else to do than travel around and look for some battles and earn some gold first. If you can't field the numbers, put points in your companions leadership when they level up, it helps greatly.
After all Alban lands were taken, it was much easier, cause there was no one backstabbing us and there is sea from 3 sides around the new territories. I wasn't asking for any rewards when taking these settlements, as they are only castles anyways, so each lord got something and they were able to field larger armies. Most had 300-400 men, and I once saw Halfdan going around with 900

By this time, Gwynedd had grown to largest faction in game, with like 5-6 cities, so I know your pain. But at least AI lords were much more able to help me out and even make successful campaigns on their own (I soon started refusing honor of being Marshal, as I feel it distracts them too much from guarding the new cities we have taken).
Here it was often enough for me to make unsuccessful attacks on castles/towns, just to get garrison below 100 men. This normally caused our marshal to declare campaign on the place soon.
But it was really going back and forth, until I begun donating troops to our faction - leaving 100-150 troops in freshly taken castles even when I ask no reward. You can even leave elites there, as you wont have to pay for them from then on, the new castle owner will. But normally I just dump my weakest men there. This also makes my party more and more elite after each siege as only the best remain

This method slows you down a lot, as you need to retrain over 100 men, but at least you do not have to retake the place 5 times, paying for food, for siege and for keeping morale up each time.
Once Gwynedd is out of the way it should be much easier, at least for a while, until Northumbria is so huge everyone hates them. I chose not to go for being king this time, as I find it tedious to worry about the relations with lords, who gets what fief and so on. I just want to fight and let my king decide how to handle that.
This means I keep working for Northumbria, we have all of Danmkark and Norway now and in England only West Saxe and Alt Clut remain. They are both friendly but the Irish kingdoms are now giving us real trouble, invading from unexpected directions.
I think I will take out Friese next so that we don't have to worry about that part of the world anymore
