They (Clans)consider several things in order of importance:
1: Their own fiefs and finances, no fief = easy to get, less money they have, the easier too. Clans with a fief are very expensive (like 1m-2m probably 5m+ now) sometimes and only bring thier fief if you're at war with thier faction
2: Power situation of their faction versus yours. When their faction is ****'d and you're is okay, they are easier to get. The power is the field parties + garrisons (not militia), the more fiefs and clans (parties) your faction has the more attractive you are!
3: Their relation to thier ruler and thier relation to you. If they like their king they are hard (expensive) to get and more likely to flip flop back to that faction later, but if they don't like them but have a good relation to you, they are easier and will stay.
When a lord flat out refuses you it means the hypothetical amount of money they would want to turn is just too great compared to what you posses, the devs did this so you don't waste your time on the persuasion dialogue only to not be able to get them anyways.
SO go after those poor home less clans (make some too by taking thier fiefs!) , defeat them and release after battle for +relations, hire some merc clans and you'll be getting vassals in not time (maybe...)! The more you have the easier it is to get more because you power goes up! (However having to many, like 20+ may prevent you from getting more, not sure)
Just to be clear, you cannot compensate for them having a fief or you faction being much weaker then theirs's just by having high relations. A lot of people assume so, but it isn't so. It will help for sure but they need to be poor, scared and preferably mad at king too!
Further more some changes to the importance of thier relation to ruler may have been added at some point, I feel it might matter more then in older versions.
Also, I feel that having more clans in your faction may prevent (or lower) lords from wanting to join you and prompt the "I'm happy with my liege". To me it seemed once I had a good amount of clans (like 20) other clans would never want to join even if all favorable condition were met
Also related, the ability to make new clans from wanderers is very powerful and would I suggest that after passing loyalty/security policies, you use all your influence to make clans for the rest of the game whenever possible.
Is it charm/charm perks? Is it your relation with that noble? Is it your traits?
afaik charm skill and traits effect the dialogue % chances, but not the condition of if the Clan will give you the dialogue to recruit them. It could be hard for me to know for certain though, but in a game where I had 200+ charm when I made a kingdom it didn't seems any more likely for them do give me the dialogue (then in games without charm) and I still had them all start refusing when I had about 20 clans. The charm did make the actual dialogue easier though.
How can i train skill on my companions...(steward, tactic, medicine, leadership)?
For steward you can have them be the quarter master of your party, for the others they will need to lead a party, it will be a slow steady process, keeping them with you in army and thus making them fight constantly can help though. However I wouldn't bother going out of my way to for the purpose of making new clans with them, even the worst ones are fine, they spawn 2 extra members with high skills and all in all just getting as many parties in your faction is all you need. Just more parties running amok is enough, eventually they start to make big armies and do a lot of work! Jusy make as many as you can.
If they can get married, what happens when a new female clan leader marries. Does her husband join her new clan?
The male joins their clan, so if you make female wanderers into clan leaders it has an advantage of also taking away men from other factions, taking powerful party leaders and giving them to you! Of course their male side members also marry and will take ladies in too!
I'd rather get foreign vassals ... like I've done before.
