Well, they allied together in the third game too, but Takeda was also allied to me at their own proposal. I took over Sado in the first turns, made peace with Jimbo, allied with Takeda, went to take over Noto but Takeda beat me to it by one turn (my army landed via sea right by the city and literally stood there as Takeda just swooped in and grabbed it. Rather than break the alliance, I retreated. As Ashina was being smart while I was away and declared war (they did the exact same thing in a previous game), I erased them from history and took over Fukushima and Shimotsuke. Much to my horror, Hojo then promptly declared war on me, after a few ninja omens from them. They blockaded my Fukushima port with a mighty navy (my more modest one was busy with pirates along my northern trade routes), and Takeda broke the alliance with me, siding with Hojo but not declaring war. I retreated from Shimotsuke as Hojo had a formidable full-samurai army incoming, my main army complete with Daimyo retreating to Fukushima where I had a few more ashigaru left and another in the making, every little bit counts. I was allied with Date for a while but they broke off the alliance, and throughout the campaign I would try to make an alliance with them, they would demand 600 gold, I would accept and then they would just cancel the alliance in the next turn or two.
The battle of Fukushima seemed rather hopeless as I was up against a full samurai army with three generals, my army was maybe 1/4 samurai, but my ashigaru were mostly level 4 experience. Their army was also larger by two units than mine. In the colossal castle battle that ensured I managed to somehow pull off a Pyrrhic victory. I pursued the remnants of the Hojo army with my own crippled army and killed it off to the last man. My army remained in Fukushima for a while to replenish.
Meanwhile even before the battle of Fukushima took place, right after Hojo's war declaration, I had another much more modest but quality army attack Hojo from the direction of my capital and take Kozuke. Made up of three katana samurai, a unit of warrior monks (the mission reward for researching essence of the spirit), and 2-3 ashigaru units, flying on the wings of my my new found confidence and Hojo's military catastrophe, from Kozuke it retook Shimotsuke and also rolled over Hitachi, Musashi and Shimosa, encountering light resistance as what ever Hojo had left it tried to use to retake Kozuke. It was a small army of four samurai units, but my garrison in Kozuke were two ashigaru units. Combined with retainers, again somehow against my own expectations this turned into a pretty nice victory. Bleeding all over the place, Hojo finally begged for peace just as the Date snakes declared war. Even though I'd have loved nothing more than to run Hojo into the sea completely, I had to accept as I need to fight Date now while Hojo isn't much of a threat. Hojo has three tiny coastal provinces left in Kanto/Chubu, but still retains a mighty fleet.
This is how far I got today. I was lucky that Takeda never joined the fray on Hojo's side as it has its own Ikko Ikki troubles in the west. My plan is to now boost my Fukushima army in anticipation of Date, as well as keep something on the border with Hojo, and if funds permit, finish them off sooner rather than later. I developed a lot of Chi before I switched to Bushido, all the way to Terrace farming and Essence of the Spirit before I went for strategy of offense/defense and beyond. I'm still strapped for cash most of the time, my income is about 1500 koku and my treasury anywhere between 500 and 3000 per turn. I had a whooping 8 rice units at one point, with no money to spare for upgrading provinces. I upgraded the gold mine on Sado as far as it goes, have two trade nodes and terrace farming in most places. Still for a long time there weren't many partners to trade with as my land neighbors were not nicely disposed towards me, my southern ports were blockaded and many northern sea trade partners prone to being conquered. Perhaps I should finish off Hojo and try to take care of Date while Takeda and Ikki fight each other, I don't want to trigger realm divide with these slimy Date behind my back.