You're not going to want to hear this, but you'd be way ahead just waiting until your youngest has graduated from high school before coming here to live full time. You can holiday here during school breaks in the meantime. Why? Online classes suck. Your oldest will not be able to legally work here. You'll have to use an agent for any visas.
Next to zero chance of you finding a legitimate job here in Thailand. Find work in your country while taking classes to improve your employment opportunities.
I don't think that you will have a problem at all. You haven't been staying in Thailand all that long. You simply want a little more time to finish your cycling journey. I'm a Warmshowers host in Trang, so I fully understand what you are doing. We host around 100 cyclists per year here. Our latest ones were last weekend.
You can always try calling. But my personal experience with Bangkok bank is that everything has to be done at the original branch where you opened the account.