What is the ruling on a wife accepting a job with a forged certificate of experience, while being coerced by her husband who forces her to work to cover living expenses and threatens to make her life miserable?

A husband is not permitted to force his wife to work, because financial support is solely his obligation, especially if the work depends on a forged certificate. This falls under the forbidden testimony of falsehood. The wife is not permitted to obey her husband in this matter, and she must take her case to court, or seek divorce if she is unable to do so. The husband must know that sustenance comes through fearing Allah, and that Allah provides for those who fear Him from sources they do not anticipate. Sustenance is preordined, and no soul will die until it has received its full provision.