How can a disobedient wife living in a Western country be divorced, given the impossibility of applying Sharia law, the fear of legal and financial repercussions, and how should the custody of the daughter be handled under these circumstances?

The tribulation you are experiencing with your wife necessitates praying for your relief, and for her repentance and righteousness. Seek out righteous women who can influence her, and do not despair of Allah's mercy. Divorce is in the hands of the husband and does not require the wife's knowledge, and it is recommended to have witnesses for it. The deferred dowry remains a debt upon you if you are unable to pay it. As for your daughter, be keen on communicating with her, caring for her, and guiding her, while being mindful of the danger of residing in lands of disbelief.