Is it permissible for the healer (raqi) to order the female patient to control the jinn inhabiting her and go with him to fight the jinn folk with a sword, and to seek the help of Muslim jinn with armies to fight the jinn inhabiting her?

Whoever undertakes the ruqyah (definition) (exorcism) of someone afflicted by possession or magic must adhere to what is prescribed, namely recitation from the Quran, and lawful supplications (du'as) and remembrances (adhkar). They must avoid actions similar to those of sorcerers and charlatans, as these are closer to superstitions. Ibn Majah narrated from Uthman ibn Abi al-As that the Prophet, peace and blessings be upon him, struck his chest and spat in his mouth, saying, "Get out, enemy of Allah," three times, to treat what afflicted him in his prayer. Therefore, things like those mentioned in the question must be avoided.