asked, have you actually been to Thailand, and know where you plan to stay?
Are you remote working for yourself? Or remote working for a company? The requirements are different for each. And if you plan to work as a teacher, that cannot be done on the DTV.
Will your oldest still be 17 when you come? I think they would be considered adult at 18 (Can someone confirm this??). The requirements might be different for them.
Just banks being overly cautious. Banks have a term called KYC. "Know your customer". Every few years or so, things like this come up. It can be irritating, but better than being victimize by fraud or unknowingly facilitating money laundering/illegal activities etc.
, a visa that allows you to stay for whatever timings you require. In reality, visa exempt entry should not be used as a method to live in Thailand. In the past, it WAS used for this purpose. Thailand has started to crack down on this behaviour, especially if you show no real proof or activity of being a true tourist.
, your statements are confusing and conflicting. Americans still currently can enter 60 day exempt. If you want to stay longer than 6 months, or keep leaving and coming back, Immigration would suggest you look to get an appropriate visa.