You have to discuss with your school and with your local Immigration Office if you all are able to meet the requirements to convert your Visa Exempt Entry into a Non Immigrant B visa.
IF you use the Non Immigrant B visa and your family the Non Immigrant O visa, you all leave and come back every maximum 90 days, the visa stays valid until the day mentioned on the visa.
You can not change the reason of your Non Immigrant B visa, so you have to apply for a Non Immigrant O or O-A or O-X visa abroad and your family again for the Non Immigrant O visa based on being dependent, get 90 days of stay and after 60 days apply all for the 1 year Extension of Stay based on the same reason as the visa's.
as Foreigner you visit the Immigration Office to apply for an Extension of your temporary stay in the Kingdom, you need some documents and the fee for this application.
The Immigration Officer has a few options to do his job:
1. He agrees with your application and make a stamp in your passport with a later date.
2. He dis agree with your application and hands back all the documents including fee and tells you, sorry but the application is incomplete or you are not legible for this Extension.
3. He stamps the passport with Under Consideration and you have to come back on the mentioned date to get the rest of the time you asked for.
4. He not approve your application, stamps your passport, application not approved and gives you 7 days to leave the Kingdom.
Alternative is the Non Immigrant O-A (long stay) visa (retirement visa) which is valid for 1 year and gives you during that year a 1 year of stay on entry in Thailand