Praise be to Allah, Lord of the Worlds.
Working in beauty salon industry is permissible since it is a lawful business. Rather, Sharia encourages a wife to beatify for her husband. However, the wife may not be able to do this on her own. Therefore, she needs someone to help her in that, and thus it is good to have qualified beauticians so long as no violations of Sharia are committed. And Allah knows best.