Pure Mathematics Vs Applied Mathematics Job Prospects

I'll be the cynical response. Give it up. You have very low probability of gaining a full time research position in pure simply because online education is going to be making radical changes with how education is administered. Realistically you should aim to industry. A PhD can train you to be quite excellent in areas outside research math.

Research positions come from folks with lots of publications, so say you finish at 33, you will need to publish great works, each work takes 1-2 years. So 3 publications puts you around 6 years of work; now that is around 40 years of age. In the mean time you will live frugally. That is a tough shot there. I argue to aim more well-balanced, and aim more realistically by questioning your expectations and responsibilities and work/life balance.
If you deny my cynicism and pursue your advanced research, but then start to notice 1)marriage tension 2) neglecting time with child 3) inner / emotional tension

then it is time to refocus on a balanced life.

Do what you like best, anything else is just self-torture. If you are good at it, you'll succeed. As Manos' answer says, just make sure you have work near the area of ultimate interest. Look for a position not only in the US, there are plenty of good universities elsewhere.

Here is what I believe:

First of all, do not abandon your dream of doing research in pure math. This is a long road and you can build it slowly and consistently. For this reason, and since you have a family to support, I recommend you solve first the survival problem, i.e., get a well-paying job e.g. in an applied math department or in an electrical engineering department. This will provide you with the psychological strength to pursue research directions you wish, without having much pressure. Note that pressure might turn your love for math into a nightmare. Finally, since you are only 32, you could achieve a position in a pure math department later in your career. I think Weierstrass did not become a professor until his forties :)