This are such great in-depth question to be asking so I commend you for really giving this some serious thought and research. I am going to answer the questions that I know about and can however, as I do not live in Dallas I would not be able to help with those specific questions.
What is the work/family balance like as a working chef?
You are at a great age for working in a job that is all about working with your hands and working longer hours, however, the fact that you are married and have a child on the way (congrats on that BTW) makes it harder to devote to working such long and hard hours that the kitchen and the food industry commands. It is not that you are not capable because of family but because the hours are really not good for family life. That being said, I do know of a few couples with children that made it work beautifully and even got their kids involved in the food process as they got older to make it a family affair so it will be all up to you and what you are willing to sacrifice for the job at hand. The hours are long, approximately 10-12 hours a day sometimes shift work or split shifts. It really all depends on where you work though.
Will I be able to support my family with a job I may get after culinary school?
Although I will give you a very black and white answer of NO, there are always going to be people that will dispute this. The reality is that pay in kitchens is crap. It starts at minimum wage (no matter if you take schooling or not) and you have to work crazy hours and gruelling conditions to make it up the chain. If you do the research into how you wish to grow your career in the culinary world and where you are going to apply at to do that then I could see you making a better wage then the average "joe" in the kitchen. If you work for a government house, correction centre, hospital or school this will be different based on types of unions, associations, etc.
What can I do to find out if I will even enjoy a career in cooking? I can't get a restaurant job at the moment and I don't know if I'll have time to go to any classes.
You are in the military mate.......use it for all it's worth. There are some of the best kitchens for learning in the country on base so go to the kitchens and ask around. If you can, volunteer or ask to "stage" a day if possible. You might have to do this on your days off but worth the time spent to find out how a real kitchen works! Also, I would recommend getting some amazing reading textbooks or reading material to help you in your own kitchen to expand your vocabulary and learn some of the techniques taught in school. There are some great posts from previous threads here:
Is culinary school worth it and will it help me secure a job? Keep in mind that with my GI Bill cooking school won't be too much of a financial burden.
So I kind of answered this previously but school should be reserved for after you have had time to work a bit in the kitchens to see if you would like to work in the culinary world and to get some experience under your wing. Going into school without experience is a waste of money and time as you will still need to accumulate work experience in the field in order to advance yourself. Just because one has taken culinary school does not mean you will be held in higher regard from a person off the street if you do not have real world kitchen experience. Home food enthusiast does not apply....lol
And finally, are you satisfied with your career in food? What does it take to be a happy and successful chef in today's world?
Ooooo.....this is a loaded and deep question but for simplicity sake I will answer: YES for satisfaction. The latter part is all on one person's unique perspective, not a lump-it-all-in experience. I am going to say that is takes drive, perseverance, a goal oriented & flexible mentality, be an avid learner, creativeness, business or entrepreneurial savvy, peopling skills like no other, the ability to teach, have patience and to communicate effectively.........and ultimately LOVE what you do!
Now I have a question for you. Why would you not continue on into civilian avionics, aircraft mechanics, car mechanics or heavy equipment mechanics?? This all pays extremely well in the right job but even minimum wage in these jobs is way more than you would earn in a kitchen at the highest level.Earn some good money, put some away for a rainy day as well as some savings for your family and when you get a wee bit older and so are your children older, then look into the culinary world or even go into business for yourself. Keep practicing at home by using the culinary textbooks, "stage" once and a while, when you have the time, at your favourite restaurants and accumulate your experience that way over the years while making good coin. Just a thought