There's no simplest method for your situation. There's only one visa that is available to you that would legally allow you to work remotely from Thailand (to continue your trading) and that is the DTV. You can get DTV for your wife and your kids as being dependant on you. If your daughter wants to work in Thailand she would need a different visa to allow her to do so but she has no experience, no skills so would find it virtually impossible to find someone to employ her at a salary that would many times higher than a Thai person would receive
There can be a number of reasons you can't convert. Your immigration office isn't allowed to issue a 90 day Non-O visa. You don't have money in a Thai bank. You don't have enough time on your entry stamp to do the conversion. In all cases the solution is to travel to a nearby country and apply for the 90 day Non-O visa there
Depends what your looking for, if you are healthy you might just stick with your travel insurance but be aware it won't cover general health issues. If you want health insurance then shop around, I find AIA very good but the broker is more important than the company in my view. A good broker will look after you, they can solve all kinds of problems, just as an example I was sitting for hours in a hospital waiting for them to resolve payment with my insurer, I eventually got fed up called my broker passed him over to the hospital and everything was resolved in 10 minutes
Be aware that they may ask to see how you plan to support yourself over the lifetime of the visa. But I guess it will depend on what you mean by well over 500k