The other detail is while that may be personal income for the nobles, they are expected to use that income to improve their family's standing. So bribes, parties, spies, bragging, tech theft, etc is all expected to be done by the Dukes.
I.e. the players are doing an Objective Raid, and the GM has put an extra item on the map (a secondary objective, but still useful). The PCs have to stay longer, taking more damage, and the only ones that benefit are the nobles. The nobles would then use part of their monthly allowance to pay for the extra damages/ammo used, but they managed to rescue a VIP, or just helped some civilians get to safety (merchants may be obsessed with the bottom line, but a Duke risking his life for a child is great propaganda).
Or the PCs have to meet with a potential hiring agent. Normally it would be the PCs trying to shmooze up to the hiring agent to get a better deal. The nobles have the retainers who can identify items that the agent has always wanted, and will be sure to have them present (rare wines, certain foods, etc) to give bonuses for rolling the Negotiation tests. The agent feels that they are the ones who have to impress the PCs (they have a pair of Dukes!) and will correspondingly offer better terms.
Based on "What Means to be a Successor Lord", the noble PCs should try for the following:
* possess an inhuman ambition; a ceaseless, insatiable hunger for power, respect, authority.
* every action, every word pursues power, accumulating it, storing it for the future.
* each C-Bill and moment of time should be spent accumulating power however possible
* know the people they are going to meet, and what their strengths/weaknesses are
* have a network of people who are capable of handling situations without his direct intervention (so he has free time)
* find/cultivate the right families to marry to improve his family's position (marry the power)
Oh, and their peers are people that do the same thing. Expect smear campaigns, spies sneaking in, rivals taking credit for what the nobles do, tipping off pirates, etc. They will not actively help the enemy, but they will keep the noble busy with small details. Expect their rivals to be constantly trying to seduce away their potential marriage partners, taking the mercenary contracts they need, buying the assembly line products, etc. All sorts of stuff that will strengthen the overall realm, but weaken the PCs family. The PC will need to do the same, plus doing his best to point his rivals at someone else so he has some breathing room, and eventually getting them on his side. He has to do all this while not making enough of a stir that his Lord cracks down due to the disruptions being caused.