Jebbie, I'm in my mid-to-late-40's so I understand exactly what you are saying about the insurance issue. I also have two children who need insurance as well. For us, we were fortunate enough to sell at house at the peak of the California real estate market so we are able to supplement our Chinese income with our investments.
Our in-China income is more than enough to support our family of four in-country. Our university pays for our air tickets to/from the US, but not for our children. Our China income does not provide enough for their tickets and for costs of visiting the US each year. However, we work for local universities and not in the private sector. Our investments cover our Stateside expenses, as well as our insurance costs.
You may want to consider finding an international insurance company that would cover catastrophic events like a serious illness or something that needs additional attention. We pay for our annual check-ups in the States and haven't had to make a claim. I pay for my own mammograms rather than filing an insurance claim. This keeps us "off the radar" and keeps our insurance costs low. Additionally, I've used SOS services in Beijing a couple of times and the one time that I needed additional tests, etc., I had it done in Hong Kong. Much cheaper than the States.
If you are hired as a "foreign-hire" then your cost goes up significantly for your company. You'd need to have special skills to justify that cost. However, if you are able to network your skills in an area where there are jobs, then you will have a way to keep aware of the openings.
I suggest you check the American Chamber of Commerce in Beijing. http://www.amchamchina.org/jobs
Also try to find out a list of major corporations in China and log into their jobs available pages. Many international companies have need of those from their home country as well as local hires.
If you feel that teaching isn't "your thing" then it's important to recognize that. The bar for teaching is being raised each year and simply being a native speaker is no longer enough to get a job. Yes, private schools are notorious for hiring anyone and everyone who can speak English, but as education progresses, those schools will be subject to more intense evaluations, etc. I know one of the largest private school chains in the country (New Oriental) has opened in my city and charges a TON of money for a student to take classes (5,000 yuan for two weeks) and parents pay it, thinking that the cost must mean it's a good program. These same students return to their regular schools (high school) where they also have native English teachers with teaching skills and there is no improvement and nothing to show for the cost except for bragging rights that "I took a course at New Oriental."
Congratulations on your degree! If you've managed to get a degree while working, you've shown a "stick-to-it" attitude that will take you far in life! I'm sure your dream of working in China will come true. It just may take some time.