The Party Has Arrived
What follows is a quick and weapon-free way of completing this mission (with the Silent Assassin rank and in the minimum time possible, obviously):
As soon as you start, head out to the field where the dance-floor is. You'll notice a guest who is slowly walking towards the abandoned building. Follow him (there is still plenty of time for you to get your targets, but you have to follow the guide exactly so the targets show up at the appropriate places in the appropriate time). When the guest falls asleep, take his party invitation which will grant you access to the mansion and quickly head inside. [NOTE: The guest takes a long time to fall asleep, so you might as well run to the dance floor first and show off your dancing skills]
The party invitation is compulsory, and the suit is optional. You can also enter the mansion with your own suit, though the guards would mock you.
Kill John "Pappy" LeBlanc
You should kill John LeBlanc first because of time management (this will be explained later). When you're inside the mansion, just before you enter the double doors, you might want to notice the doors to your right and to your left. The one to your left leads to the restroom (it's marked with a sign saying "Washrooms", so you can't miss it) with a convenient window that leads to the back of the mansion. Here, on the outside, will be a guard sitting on a chair. He will stand up if you're not fast enough, so sedate him while you can, it's important because he may see you kill your target otherwise.
To your left will be the door through which John will enter in about 15 seconds (this is the best place to kill him and he won't stay here for long, that being the reason why you should kill him first). Stay behind the door, wait for him to enter, close the door manually to prevent the guard on the inside from seeing you, and push Pappy down the stairs as he descends, or strangle him if you lose the chance. After you're done with him, hide him in the container nearby and go back inside the restroom.
A way of killing Pappy and Muldoon from the same point is to take along you sniper rifle, obtain the gangster outfit and enter the top of the green house. Subdue the patrolling guards and unpack you rifle near window looking out onto the graveyard. Headshot LeBlanc while he is grieving over his brother, and then turn your attention to the window overlooking the wedding area. After a short wait, a gangster will start the wedding. When the couple are safely in public view, shoot the insane groom at whatever time suits you. The Customized WA2000 is good at this, as it will leave a very tiny trace to your shooting.
[NOTE: If you run all the way, you can slip into the kitchen and poison the cake before going to the restroom. That will take care of your other target, and you won't miss your chance to push John down the stairs.]
Kill Buddy Muldoon
Buddy will spend much of the start of the mission wandering around the mansion, occasionally slipping into the kitchen to sample the wedding cake. However, after the ceremony is completed, he will be attached to his bride by the hip and will be almost impossible to get alone, limiting the options.
The Poisoned CakeExit the restroom and go through the door directly in front of you (remember that this is a restricted area, so make sure nobody is inside). If you're fast enough, you should be able to enter the room while it's empty. Quickly poison the cake which can be found in this room, and run back to where you started the mission. When Buddy finally dies, you're free to escape. This method will take a while to work, so if you want, you can prepare the cake first then proceed to kill the other target. Alternatively, the cake can be hidden with a RU-AP mine, not recommended for stealth approach, but viable if you're out of options.
The Falling Chandelier
Buddy can also be killed through an accident. Way up in the attic on the third floor of the house, there are two winches that are connected to the chandeliers in the dining room. Place a mine on the winch on the left, as that is the one that hangs over the piano. Open your map and watch the red circle that signifies your target. Wait until it lingers in a specific spot in the dining room. That is Buddy messing around with the keys on the piano. Pull out your detonator and set off the bomb. The chandelier will come crashing down on the unfortunate groom, killing no one else in the process!
Ensure the Bride's Safety
This objective is already marked as completed since the beginning of the mission. Unlike the "Protect the Politician" objective in the mission The Murder of Crows, you don't need to worry about the VIP's safety as long as you don't kill her yourself.
You can either escape using your own boat or the priest's boat (which requires his key). For the sake of completing the mission using the way of this walkthrough, you'll want to escape using your own boat (just return to where you started, check the map if you get lost).