Is it permissible to wear a head covering (taqiyah) to protect oneself from the the sun due to health issues, knowing that the husband considers it an adornment?

If a woman needs to wear a hat to protect herself from the sun while adhering to the lawful hijab, there is no harm in that. The husband's assumption that it is for adornment does not prevent her from wearing it, because she has not worn it for adornment but out of necessity and to avert harm.