Will your child be going to school in Thailand? If so, ask the school they will be attending what's involved. Normally, the school handles the paperwork. Good luck!
Seriously, you will get different answers at different banks AND it can differ with location too!
We were told we had to have a bank account to get retirement visa, but told by the bank that we had to have retirement visa first. It was a very frustrating catch 22.
If you go to a bank in a high tourist area, your chances are better.
Please be aware that if you don't have an IDP or Thai license, your health insurance will NOT cover you if in an accident. It will also not cover if you're not wearing a helmet or have been drinking. This is info that every tourist should know.