To begin this mission, you will need to go to Ponsonbys (marked on your map as "M") and purchase a tuxedo. It is on the rack to the right of where you enter, and it will set you back $10,000. Meet Jimmy outside once you've bought it, then get in the limo. Once you arrive at the theatre, go to the red carpet for a cutscene.
After a short cutscene with Devin, you will need to rush home, so grab the car behind the limo. You will have two minutes to return home, which should be plenty of time. As soon as you get inside the house, you'll see a mercenary struggling with Amanda, so shoot him in the head. Head upstairs to Tracey's room and you'll see her being held hostage by another enemy.
It can be a bit tricky to get this guy, as he isn't exposed too much, plus he will shoot Tracey in a few seconds if you haven't killed him. When you get to Tracey's room, activate Michael's ability, which should give you more time and a better shot. You now need to clear the house of Merryweather mercs, so head downstairs.
There will be some that come through the front door, as well as some in the other rooms of the house. Make your way to the back door, then head outside and start killing the mercs there. Make sure you get some nice cover to protect yourself, then take out the rest of the Merryweather thugs. Go to check on your family and watch the cutscene through to the end of the mission.