It all depends IF your local Immigration Office is allowed to perform this conversion into a Non Immigrant O visa, if not if means travel and book hotels to stay near an Office which is allowed.
Most easy option is to provide the documents and get the visa before travel, not sure why you choose for retirement as you also have the option of being married with a Thai Citizen.
And based on marriage has less financial requirements if you apply for the 1 year Extension of Stay.
You apply at your local Immigration Office, just go there and ask the hand out with requirements. Copy them and tick the list, when done visit again to apply.
Not an IT expert, but could it be that user name and password are saved in your browser and automaticly filled in. Try to clear those savings and try again.
If you want to stay long term with your child in Thailand, at the age of 6 the child needs to go to school. Contact a school and apply with documents for the Non Immigrant ED visa for the child.
Every foreigner needs a visa, that there is no fine for children until 15 years of age, does not change the rule.
Problem? The regulations of the Thai Immigration if you like to transfer a 1 year Extension of Stay into a new passport are set by Immigration.
You get from your Embassy a letter that the new passport is a replacement of the old passport with the passport numbers, you copy old passport and ID page new passport and Immigration will than put a new stamp in your new passport.
Always good that people ask to be sure, but every 90 days you went with the school to Immigration and signed the STM2 form, see example.
Show this to the school and maybe they will ask Immigration to understand what it means to inform Immigration when the reason for the stamp change. a Change is ending education in your case.