What visa options are available for a family with a 4-year-old planning to stay in Thailand for 1 year?

Depends what the purpose of your trip is. If it's leisure then the elite visa is about your only option for a year.

Why's nobody mentioning the Elite visa

You will not be able to stay in Thailand for a full year as a tourist without leaving and returning at least three times. You all apply for multi-entry tourist visas that are good for six months after you get them. You get a 60 day entry stamp each time you enter the country, and can extend that by another 30 days at immigration. If you time your border bounces right, you can stay almost 9 full months. At the end of this you go to a Thai Embassy at one of the surrounding countries for a few days and get a regular 60 day tourist visa that is good for 60 days and can be extended for another 30 days. This will take you to almost one year. At this point you just cross a border and immediately come back with a 30 day entry stamp, completing your full year. Any other option would require you to work full time, or go to school regularly for the full year, extending your visa every 90 days, and the school providing the documents proving that you are going to school, and passing your classes.

When it comes to immigration matters, best to start with an official source, not FB.

Have you bothered to look up your visa options on your own first? Just a simple google search will reveal what options you have available to you. Start there.

Depends on your age and what you would like to do in Thailand. May I ask?

You don't get to decide how long you stay, Thai immigration tells you how long you can stay.

Unless you're over 50 years old, your options for a long term visa are limited to Education visa or official work permit / visa