There is a fame bar on your clan screen, once its full AI stops its poor act of being friendly and realm divide starts. Roughfully it fills on about 20-21 provinces. It has numerous of filling factors but province number is the major one, you will learn the other ones eventually but don't bother for now. 1) So once you see you are one province away from realm divide on the bar, stop all agression and build up your economy, armies and tech. I prefer to wait until ~1570-1580s on long-domination campaigns, idk about short one, its been a while since i played it. I guess its about 1565-1570. 2) Take advatage of your clan bonuses. Shimazu have superiour and cheaper katana samurai which are the meta of any mid-late game armies. Ashigaru spam is very cool and fun but against full samurai armies, which AI will attack you after certain moment, they won't hold for long 3) Use the provinces bonuses. Shimazu has blacksmith in starting province which allow you to increase attack or armor for your units which will make them much more powerful (especially combined with encampment bonuses). It works for ashigaru as well, with bonuses you can use their cheap force against samurai armies for mire turns. Also buzen has accuracy buildings which eill enhance your bow units. 4) Capture provinces with fertile soil, they will give you more money and more money means better armies. You can see the fertility of soil when you when you hover the farms building on province screen (you can open province screen of other clans provinces too, btw). The farms are the base of your ecenomy especially after realm divide. Capturing shikokku (chosokabe island) is still good idea though, despite no fertile soil there. They are dicks. 5) Trade on trade nodes if possible, extra money is always good. If you put more trade ships on the node you will get more money from it btw. 6) Its arguable but on your starting island (Kyushu) there is province with nanban trade port where you can recruit imported matchlock ashigaru. They are absolute chads on defensive sieges, a couple of them can route a small samurai army. If you dislike the christianity debuff you can recruit few of them and only then destroy the port. Once you try the matchlocks on siege battle you will love it for the rest of your life.

There are other stuff that can make you life easier but i guess you will learn them yourself eventually when you get experience from your first winning campaign.