The big question is essentially whether it's a reasonable idea to have a move that only works in conjunction with another move.
You mean like
help of interfere? There's certainly precedent for moves that affect other moves, or moves that spawn other moves. But in all the cases I can think of off hand, it's never the same character rolling twice, and I think that's probably by design.
Apocalypse World, in all its various incarnations, is very good at cutting things down to the minimum number of rolls needed to tell the story. So instead of asking if it's reasonable to have a move that only works in conjunction with another move, maybe the question should be, "does this move add anything to the story?" or "what are the consequences of success or failure with this move?" or maybe "could the effects of this move be accomplished by other means such as adding or subtracting tags from something or someone?"
It is of note that when AW does this, it's not an additional move, it's essentially a stat substitution move. Look at the Brainer move that allows you to
go aggro with your mind as an example.
Agendas definitely are supposed to be secret and that's not the problem; the problem is that some people just seem incapable of coming up with more than 1 thing their character cares about.
Have you looked at the state of political discourse lately?
Most people seem incapable of caring about more than one thing.
I think the problem is that the agendas are too nebulous. Nebulous is great in your head. But where the rubber meets the road, nebulous can be less helpful, especially when everyone is being nebulous.
What makes this doubly difficult is that the world is not defined. It's all well and fine to come up with a motivation of "become Grand Vizier" if you know that the position of Grand Vizier exists in the first place. But what about, "become Regent?" Who is king (or queen)? Who is in line for the throne? How old are those people? How is succession determined? Is it straight-up primogeniture, or is it more complicated? And more broadly, are other ranks and titles hereditary?
Does the monarch rule completely by fiat or are there limits to the sovereign's power? Is there a privy council? A parliament? How is membership in these bodies decided? What constitutes "power" in the current system of government? The ear of the king? A large voting block in the assembly? Wealth? Military might?
Similarly for anything related to wealth: what positions provide opportunities for creative accounting? How do taxes work? Are there guilds? How do they work? Do they have representation in the government, and if so what does that look like?
I've been a player in this kind of game before, where the GM wanted intrigue but didn't give us any detail for how the world worked. It is paralyzing because you a) have no idea what's possible, and b) have no idea what steps you need to take to get there.
I'm not saying you need to create every last detail of how the setting works and make the players drink from the firehose (because that can suck too). But I think what you need to do is put some more thought into simplifying this and come up with some lists of useful or helpful options to spur your players' creative juices. I would also separate things into primary objectives and secondary objectives. Or maybe long-term and short term goals.
So for instance, if my long term goal is "achieve wealth and splendor," there are a variety of ways I might do that. Corner a local market, engage in risky deals, steal the fruits of others' labors, gain position or office that is ripe for abuse, etc. Alternately, if my long term goal is "cover myself and my family in glory" then I might want to achieve military honors, serve with distinction, remove an embarrassing relative from office, elevate a deserving relative to power, foil a plot against a powerful official, or be seen to be selfless.
I am guessing that if you give your players a laundry list of basic ideas from which they can start, they'll fill in all of the details and motivations you're really after. It's far easier to give someone a list and say, "pick three" than it is to have people make up three fully fleshed out motivations from whole cloth, especially when they know little or nothing about how the world works. It will also make it easier for the GM to see the areas where things overlap. So if I'm trying to "gain a position or office that is ripe for abuse" and you are trying to "elevate a deserving relative to power," then the GM can set it up such that both of us are jockeying for the same position. We'll happily work together to disgrace and bring about the downfall of the guy who currently holds that position, then ruthlessly oppose each other when it comes time to fill it, which is more or less the kind of interplay it seems you want.
More broadly I have an issue with your experience mechanics. Both of the ways of gaining XP that you have outlined (deepening a Bond or making progress on an Agenda) are up to the GM. That is completely counter to how the Apocalypse Engine works, where the
players are in control of how they gain experience. In AW if my Hot is highlighted and I roll it, I get XP. Even if it's a -2 and even if I fail. If my Hard is highlighted, when and how I resort to violence is
my choice. The system you have designed here is pretty nebulous and doesn't allow for player input or control. I think you need to scrap it and go back to the drawing board. At the very least I'd give the players the ability to change each others' Bonds much like you do with Hx.
Also, why no seduction? How can you have intrigue without seduction?