My gut feeling is that it's going to be hard to make money without experience and connections but I'd love to be wrong. Has anyone had experience doing this sort of thing?
It will take time. The first few projects won't pay much. But that is how you start - with small projects. Then you ask the people who couldn't afford much more than a website with a couple scripts if they know anyone who needs help. And you work your way up to bigger companies. With bigger problems. And bigger budgets. Eventually, you'll see a pain point that multiple companies have asked for. Write software to fix the pain point. And expand that software into a business.
This is exactly how successful "lifestyle" software companies are built. Do small things until you find the bigger things.
Yes. You can do this by: Building lots of products and launching them and reaching out to people who are looking for contractors online and sharing similar/relevant products you're launched.
It sounds like you're describing the classic problem for getting started in a new career (no work experience & jobs like experience). The numbers likely won't be pretty for trying to get clients. For example, I know someone who is a self taught designer, and very good too, and had to apply to 100+ jobs in this market to get 5 interviews, and then had an offer from 1 and decided to end the process and take the job. Those numbers can be discouraging but it only takes 1 yes to get that first real work experience, and from there it only gets easier.
It sounds like the hard part is just meeting enough people to consider yourself qualified. A third of the work in freelancing is marketing, another third is research and/or selling off prototypes at a loss. For example, it's costly to figure out how to make an app with Google+ sign in, but it's easy to do the second time.
It could be possible to start cheap, by letting experienced developers outsource that kind of work to you for something like $10/hour. You can also look for Fiverr style stuff like assembling a Wordpress site or writing tests.
And many 'full time' freelancers (I've been one) find themselves repeatedly being 'part time' when there's a slow month.
Freelancing is hard, and is a combination of luck, timing, and seriously hard work. There is no formula. Ever.
You already have 2. Isn't the point of having kids to spend time raising them? Now there has to be a third and you have to pick up a second job so you hardly spend time with them.