Don't do anything at all. At least, not at first.
Let the PC's meet and greet the various guests. A good majority of them will be representing various movers and shakers of the country, nobles, merchants, clergy, other adventuring parties, the charmed agents of the lich dwelling in the nearby necropolis, a doppleganger or two, you get the idea. They are all there to evaluate the new local rulers and to see how they can fit into thier own plots and schemes. Have some of them make offers of alliances to individual PC's. If possible, get two different PC's to side with opposing forces. Let dinner and dance go without any major obstacles. Have as many people as possible talk to the PC's. Lots of Innuendo, Bluff, and Sense Motive checks. Drop a few hints to the hidden agendas of these people. Foreshadowing is your friend.
After the party, the PC's are no longer an unknown quantity in local politics. They will be taken into account as possible allies, tools, or enemies in the plans of the various powerful folk in the realm. Now you really let the sh** hit the fan.
Did a PC act rudely to a local lord? He'll be turning a blind eye to bandits robbing the settlements the PC's rule.
Start calling in those favors and alliances. PC's will be asked to join a coalition of nobles who are petitioning the king for something. Make it something nice and dubious, that the PC's might not actually want to happen, but can they really afford to tick off their three powerful neighbors?
A thief/assassin/fellow up to no good used the ball as an opportunity to scout out the castle. He then returns to steal something or assassinate someone. Or maybe he sells the information to the highest bidder. If you have a rogue-type PC with contacts in the thieves' guild, have them find out about this somehow. Let the party scramble madly to come up with the cash to buy the exclusive rights to the info before anyone else does.
Go nuts. Politics can make for some great roleplaying opportunities. Juggling so many NPC's and factions and plots can be difficult, but doable. I'd suggest going with index cards (one per person/faction) with a brief summary of who they are, general goals, and attitude towards a few other factions. I'd also suggest reading George RR Martin's Song of Ice and Fire novels for inspiration. Lots of nifty political stuff there (not to mention body count). Some of the later Vorkosigan novels by Lois Bujold may be helpful too. I'm sure others can point you to other good sources of inspiration.
Best of luck to you, and have fun.