Similar to the PS version, you need to go to your work room and complete the drawing (5-6 actions), set the table gently (though if Grace complains once, that's OK), and play with your kids.
When you play with Shaun, carry him around the backyard a few times until you set him down in a mini-cutscene. If you set him down early with an action, the achievement will break.
When you play with Jason the second time, you have to 'win' the swordfight by putting in actions quickly enough. If you miss one or two, it's fine as long as you still 'win'.
If you do all this and the achievement doesn't pop by the time you're in the mall, keep playing. After you put Shaun to bed at the end of Chapter 2, the achievement should pop during the cutscene when Scott Shelby's face appears. If you've earned "Good Father", you'll get that at the same time.