Do we need to show a bank balance of $30k to apply for a remote worker visa in Thailand for my wife and dependents?

Yes and you can not apply for this visa while you're in Thailand (just good to know for some)

You need to meet all the requirements one of which 500K THB or equivalent for the initial DTV - then the requirements for dependants once approval of the original DTV is granted

You need to go to the website of the embassy you will be applying at, and see what their requirements are. Each embassy sets their own requirements. Some want to see the required funds for each person, while some only want to see it for the primary person. Some just want to see the bank balance, while some want 6 months of that balance, etc.

She would have to apply, pay for, and receive her DTV first. And then you and the children could apply, as a dependent visa requires you to upload the already issued primary visa. Then you and the kids apply and pay for your visas, and meet whatever the requirements are for the embassy you are using.