What are the requirements and process for extending a 60-day entry visa in Thailand for a family with a baby?

1900 baht,you probably couldn’t find a person that’s been denied a 30 day extension and you don’t need an extension for the baby they can’t be fined for any overstay until 16

If you are stying in a hotel, they will have registered you online, ask them tp print a copy of the lodgement, if they cant do that just take a busines card or similar with the hotels name and address, if you are in a private home or air bnb ask the householder to register you online and take a copy or a screen shot of the lodgement. and the exact address written in Thai, that just make it easier for them

"TM.30" from a place you are staying in Bangkok (which all family's names on it) is the most important thing.

That should help you

In Bangkok you can apply for an extension when you have 45 days or less left. There is no requirement for an exit ticket for an extension. Each extension is 1900 baht per person. Children under 14 cannot be banned for overstay and cannot be fined for overstay. Many people don't bother getting children under that age an extension.

If you arrived with a visa you bought from a Thai embassy before you traveled then you go to Chaeng Watthana office. If you arrived with no visa and received a visa exempt stamp at the airport, then you go to IT Square Laksi office.

Here are general requirements for the extension, each office may vary.