They try to push this policy noticeably often, like they clearly want to push this specific policy. Im sure there is some reason for that, but its not just a coincidence. Also there will be joining a lot more clans to my empire, who will only add to that cost and at some point it will just be too much to have any influence on any decision. Already now I have to accept everything else they demand and save my influence basically just to prevent that one policy. For me it seems really difficult to gain back that much influence, because I dont do 1vs1 or high odds battles often. Thanks for the suggestion of royal privilege, this will certainly help a bit for now.
With influence... you need to maximise your passive gain. Having maxed out forums in 3 to 4 cities is a good start. Treat the cities well and you'll also gain supporters in those cities. Then if you make 3 or 4 parties (there's a leadership perk that allows an extra one) and keep them in an army with you permanently, you get influence for each of them too + it will quickly push your leadership skill level up. By carefully selecting policies you can comfortably get to 20-30 influence per day before you even fight, if you're lucky, or have taken ownership of more cities, that can be booster further. That's a couple of thousand influence per year even without fighting + If you have trouble, with that many parties in your faction, in your army, you can end up with 1k soldiers at no influence cost - big enough to fight many battles - that means battle influence is free of cost.
Once my influence is at that level, I start allowing votes that help big clans build influence through so that they can build armies too. I also push policies that keep army recruiting cost down. But otherwise..... you might have missed my post above... but this is my starting framework:
Get as soon as you can:
Royal Privilege: For Kingdom decisions, the influence cost of the ruler overriding the popular decision outcome is reduced by 20%
Precarial Land Tenure - The influence cost of proposing settlement annexation is reduced by 50% for the ruler clan.
Avoid at all costs:
War Tax - The influence cost of declaring war is doubled for the ruler clan.
Feudal Inheritance - The cost of revoking a fief from a clan is doubled.
Peerage - For kingdom decisions, tier 4+ clan choices have double effect, Influence cost of the ruler overriding the popular decision outcome is doubled.
I have a hunch that clans seem to push negative policies if they don't like you. So maybe that's something to keep an eye on too. But that's speculation.