What are the visa options for a foreign teacher's spouse on a dependent visa in Thailand?

Go out to Chaengwattana Section C-1 <- that's the section that issues in country 90 day Non-Immigrant Type visas. They will have a hand out that lists the required documentation to apply for an in country 90 day Non-O visa based on being the spouse of someone who has a Non-B visa, a work permit and who legally works here.

Your husband will need at LEAST 15 days left on his current stamp to apply in country for this visa. If they do not have that much time left on their stamp they can't get the visa inside the country and they either need to go to a thai consulate in another country to get the 90 day Non-O visa OR they need to exit/re-enter the country on a new 30 day visa exempt entry stamp or a new 60 day tourist visa to start the process at the immigration office of getting a 90 day Non-O visa in country

Your spouse applies for an extension which is done at CW. Or your spouse leaves the country and applies for a new dependant visa.