In: Physics
I'm considering taking a hobby (taking math and physics classes, reading attempting to read arXiv papers) and turning it into a career change. However, I have 3 kids and a wife who doesn't make a lot of money so I have no choice but to look at grim reality.
I'm willing to work hard, network with people, do research, etc. so let's leave effort aside.
What is the statistical likelihood of getting a job as an actual theoretical physicist?
As an experimental physicist, I'm not perfectly placed to answer. However, the only job as a theoretical physicist, that is, doing theoretical physics, at least as far as I'm aware, is in a research/invited/appointed post at a university, special institution (Institute for Advanced Study, etc.), or (maybe) a national lab.
That said, there are more Ph.D. students coming out of physics than there are university positions for them to occupy. For a short version of why it's unlikely to get a job as a theoretical physicist, take a look at the Many Applicants, Few Academic Posts on page two of this article: http://www.scientificamerican.com/article.cfm?id=does-the-us-produce-too-m&page=2 (the rest of the article is worth a read as well).
The outcome of the situation is that a lot of physicists go into industry or other fields. But, industry doesn't use theoretical physicists as theoretical physicists. They use them in Wall Street for solving complex equations, for example, but not for physics.
I'd add to this that the competition in theoretical physics is rather significant, since it takes quite a special brain and a lot of training to make real headway on the deepest problems of the universe.
So, unfortunately, I'd say that the likelihood of getting a job doing theoretical physics is rather slight. And, given your economic constraints, it's unlikely you could afford to go through the low-pay period of a Ph.D. (a requirement) and a post-doc (in practice, also a requirement) in order to get an appointment in the field. If, on the other hand, you want to learn theoretical physics, even get a degree in the field, and then use that knowledge elsewhere (Ph.D. only), you might be able to swing that.