Is it permissible for a husband to allow his wife to remove her hijab, knowing that she suffers from severe psychological and physical problems due to wearing it, and threatens divorce if the situation continues?

A husband is not permitted to allow his wife to go out adorned (تبرج). If the wife does not respond to her husband's guidance and refuses to comply with Allah's command regarding the hijab, then divorce is recommended; it may even be obligatory, as there is no good in a woman who rejects the obligation of the hijab.