non O can be applied for from anywhere, including inside Thailand. It's the non OA that must be obtained in your home country or a country that you have permanent residency.
Don't listen to all the fear mongers. No your account won't get canceled, yes you might be called in for a KYC interview or updated ID. I've had my account with SCB for 15 years opened up on a tourist visa and the same with my Bangkok bank account only opened up a year ago on a work permit, and now I'm on a DTV. Neither branch manager told me to worry about anything they're looking for criminals.
Leaving is better than the option of an in-country extension and the 0.4 meters of paperwork that will be requested. Regardless, you'd have to leave after 360 days anyway.
elaborating a bit on Andy's reply yes you'll have to show proof of parental rights/birth certificates over the dependents just like you will show proof of being a legal spouse for your spouse's application