You asked this earlier in a different group, the answers you get here aren't going to be different. If you can manage to get the paperwork from the new school before you your kid stops studying at the old school then you both go and cancel your extension of stay on the day the kid stops studying and immediately apply with the paperwork from the new school. If you can't manage to align them then you cancel the current extension for both and start over
So are you currently on a tourist visa or visa exempt entry? If so it's a question of burning through shoe leather and try every branch of every bank until you find one that will open an account for you. Make sure any bank that will, will also provide the guarantee letter for immigration, it's not currently clear if Bangkok Bank will do that or not in your situation.
Those saying they've done it frequently are either talking historically or are not maximising the time they spend in Thailand Visa exempt. Simple fact is you can no longer expect to get stamped in if your history is not that of a typical tourist. Ultimately it will be down to the immigration officer you stand in front of