Melissa, as you can see, not a whole lot of positive responses here. The thing is, it can be done, but not everyone can do it. It actually really pains me to say it because I am a huge feminist and I believe in most cases that everything is achievable, but this is definitely one area where you can't be great at everything. Someone else said it above: something has to give. It really matters what your priorities are; if you want to upgrade to captain, work for a major, be insulated in case of furlough/bankruptcy, etc, it requires a bit of flexibility. Children, almost by definition, eliminate all flexibility in your lifestyle. Now, before we assign this as a "woman's problem", I might add that I work with a lot of oblivious men who believe that a little Skype while they're away and a paycheck every two weeks means they're good family men. Trust me, the kids miss their daddy, too (and the spouse probably isn't thrilled that hubby is at the hotel bar enjoying a nightcap while she's dealing with three little ones by herself). Frankly, if you want to be home for PTA meetings and ballet recitals and see your child crawl and speak for the first time, this isn't the job for you. Being away from home for 4 or more days a week takes a toll on any relationship, and it will certainly be many years before you and your S.O. could be senior enough to get more time at home.
There are no easy answers for how to be a mom and do this job, the short answer seems to be that it takes a village to raise a child. Again, I know friends who make it work with both being pilots, but I can see the cracks in the thin veneer... One Mom had a meltdown during a trip when she found out Dad's plane broke and he didn't make it home and the baby had to spend the night at the babysitter's house. I personally could not square the fact that if my airline husband and I had kids we'd rarely get to see each other bidding opposite schedules to make sure someone was home, and we decided it wouldn't be fair to each other or to the children. So we opted not to.
My priorities have changed significantly since I began doing this job, yours probably will too. My advice would be to wait on kids, try out the dream job. You might decided after a few years that the job isn't your dream anymore and you can drop it and find something else that might give you a stable foundation for your family... You can't give back the children when you find they aren't compatible with the career you love.