Can I Change My Dependent Visa to a Work Visa While in Thailand?

Okay, here we go? Important details are missing and most likely wrong terminoligy.

I guess your wife works in Thailand for longer than 90 days.

BOTH of you visited the Immigration Office and got a stamp with the text:

"Extension of Stay permitted up to xx/xx/xx"

You have to visit the SAME immigration office to cancel this Extension of Stay, you can do this in advance to give you some time to pack your bags for travel.

Before the last date you travel abroad and apply for the DTV Workcation.

You cancel your current visa first and apply outside the country. Considering how unstable schools are here, how bad foreign teachers are treated and fired for the smallest things you won't need that risk