Even though the whole regency system is fairly shallow (especially in vanilla), GOT mod makers quite decently improved on it in this mod. Firstly on the whole title hoarding ambition of yours. As a regent ,if you try to interact with yourself you might notice an option which is titled "Give yourself liege's title" ,which unremarkably , does was it says (it allows you to take any of your liege's none king tier or above+none main titles which he holds directly), so indeed it would be a valid tactic to try to piss of your liege's vassals by removing them from council, and then hope that they rebel at some point and then,if you get lucky, claim those titles from your liege (Of course that is if he actually manages to successfully defeat those rebels and then consequently revoke some of their land). Now secondly regarding those events you mentioned, yes there actually is one pretty neat event that allows you to completely usurp all of your lieges titles but i'm not entirely sure if whether there are special prerequisites to it or how rare it is, all i can say is that it often resolves around the concept of you maintaining your regency for while.
Other than that, unfortunately you don't really differentiate from the average joe of a vassal in regards to realm wide power.Also something worth mentioning, if you have a claim to your liege's main title as his regent i believe you get an option in the intrigue menu to attempt a coup d'etat, also from time to time you might get options to steal from the realm's treasury but as i've noticed those sums are more often than not trivial and not really worth potentailly giving your liege an imprisonment reason (which he can use when/if regency ends).