Playing as Tywin Lannister, not only the Tyrells, but the Westerlands as well is not at war with Stannis in ACOK. This can definitely not be wad.
AI Joffrey does not ask to honour the alliance (as Joffrey himself, you can call in Tywin for the second war), and as Tywin himself you cannot join another of his wars as you already participating in the war for northern independence.
Conclusion, The Westerlands need to be in both wars at the scenario start- in my first two attemptst I had to watch Joffrey getting destroyed by armies from the Stormlands, while my 25k men were camping in KL, but could not take part in the battles.
Even with Robb Stark killed and all his 30k men slain, it near impossible to gain 100% warscore (unless Robb fails really hard and gets captured) and end the war in time to join the second war before the Iron Throne army gets demolished.
Tyrell event on the other hand worked fine for me so far, didn't test it in the latest version though since clever Joffrey decided Sansa is his great love (and guess who became LP of the North, revolted and rots in prison now since over a decade, popping out Lannister babes