Can I Apply for a Non-O Visa Based on My Wife's Non-O Visa as a Dependent?

I think you've got your wires crossed a bit

Only ONE parent can get a non-O visa/extension based on supporting a foreign child here and that parent needs 500K baht in a bank account in their name only and to supply the required documentation

The other parent could apply for a Non-O visa/extension based on being married to someone on a long term extension of stay (called "trailing spouse")

GO to your immigration office and see if they will even issue a Non-O visa inside the country based on that reason. and ask them the documentation you need to provide to get it issued.

Not all offices will do it and with 70+ offices in the country there is no "list of documents" that will work at them all. That's why you need to go ask yourself