I have a four-year-old daughter, and I absolutely feel that she is the most challenging part of my practice. Not because she occupies so much time – though she definitely does – but because she requires so much engagement. In particular, she wants to play make-believe pretty much every moment she's awake.
There's something about make-believe that seems especially anti-practice. Here I am trying to spend my time not making myself more of a person than I am, and now not only do I have to be a person, I have to pretend to be a person other than the one I've been pretending to be all these years. It can be horrible.
So I use this as indicator of how my mindfulness is "doing". When it's "doing poorly", I feel absolutely desperate to get out of the make-believe games. And back to my own games, of course, which as you note is usually staring at my cell phone. Staring at my cell phone is primarily a way of shutting off awareness altogether, of course, and what I'm actually unhappy about is the fact that I'm being forced, by my daughter, to be aware of the current moment, when (for whatever reason) I don't want to.
If mindfulness is going well, I can remember that what is important is presence itself, mindfulness itself, and the question of mindfulness of what, exactly, is almost beside the point. If you were meditating instead of dealing with your family, you would be spending your time trying to be mindful of the present moment. So how is that any different from being mindful of the present moment while you're with them?
Switching from one mindset to the other can be difficult, usually because there is resentment in me when I'm experiencing the first mindset, and switching to the second mindset requires letting go of that resentment, and it is important to me to hold on to the resentment. If I can swallow that, then the trick is to tune in more fully to the sensations of the moment, so that my mind is filled with moment-by-moment sensory data, and there isn't room to think about how unbelievably tedious it is to play Mermaid Dada ONE MORE TIME.
If I can stay in that place for a little while, then the desperate need to turn away quiets down, and I'm able to surf along on the flow of events. Not that I ever quite love it, but it becomes possible to remember that I'm enjoying being with my daughter.
Hope something in there is helpful...
[Edit: I realize I've just restated what Chris said, but using lots more words.]
