I'm a Java developer at a large insurance company. When I joined my team, the technology was new to me, but now, its just maintenance. I'd like to learn new technologies but time always gets the better of me - Household choirs, caring for my young kids, spending time with my wife.
Does you book talk about strategies on how to develop my programming skills/technologies while balancing work/family?
That's a tough one. I don't believe in sacrificing your personal life for your career, so in my opinion you've been prioritizing the right things at a high level. I don't even believe in sacrificing fun time for career development. To me, the most precious resource we all have is our passion, and sacrificing fun is a sure way to kill it. If you do that, it doesn't matter what you learn--you're not going to be successful.
My bet is that you could find 15 to 20 minutes a day. Faced with the task of learning something new that's big, it's easy to get discouraged and to feel like the problem is too big for you to solve. But if you spread it out over a month, you'd be amazed at what 15 minutes a day can buy you. You might find yourself getting excited as you learn and voluntarily giving up something frivolous you've been doing to unwind (a TV show you don't like that much for example). But don't start there. Start with reading a book for 15 to 20 minutes when you go to bed. Or as soon as you wake up in the morning.
Or, take some time at work every day. Don't ask for it. Just do it. You know that personal development makes you a more valuable employee, so 20 minutes of learning time a day is only going to help you and your company ultimately.
Another thing to look for is stuff you don't like to do but you feel like you have to do. Ramit Sethi talks about this in his book I Will Teach You To Be Rich. He says that frugality-driven approaches to saving money don't work because people don't like being frugal so they don't stick to the plans they create for themselves. And most frugality just removes small pleasures but doesn't have a strategic impact on your finances. So, he says, focus on spending as much as you like on the things you love but then ruthlessly avoid spending on things you don't want to spend on (credit card charges, high interest rates on loans, etc.).
I apply this to career development as well. If I need time to make myself better (and to have fun, spend time with family, etc.) the best place to look for that time is on the things I shouldn't have to waste my time on in the first place. Are there rituals you've been doing for years that don't bring you any benefit? Are you doing something "fun" that isn't really fun anymore because it's become a chore? I've found that I get into these traps and there's some amount of free time there for the taking until I do a personal spring cleaning.
The Passionate Programmer: Creating a Remarkable Career in Software Development