Can you get a little bit more creative with your time utilization? Commute to work, Ride at Lunch, Get a child trailer, or a child trailer and a Tandem, ride the trainer while the family's sleeping.
Admittedly, these aren't necessarily the best training solutions. But if you can get some miles in, in a way that doesn't take away family time, and supplement those miles with some focused training, you may surprise yourself with what you can accomplish on a limited schedule.
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You could fall off a cliff and die.
You could get lost and die.
You could hit a tree and die.
OR YOU COULD STAY HOME AND FALL OFF THE COUCH AND DIE.