Female family members either travel alone without a male mahram, or they go out (anywhere) without hijaab, or both. What is the ruling on a male family member escorting the female mahrams (for example, by taking them out, driving them, etc.)?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
Firstly, this man – or others – should advise them, and he should be soft and gentle with them when admonishing them out of mercy to them.
‘Aa’ishah narrated that the Prophet said: “Whenever gentleness is found in something it beautifies it, and whenever it is withdrawn from something it leaves it defective." [Muslim]
It is hoped that they will benefit from his advice and he would be the reason for their guidance to the truth, and there is a great reward in that.
Abu Hurayrah narrated that the Prophet said: “Whoever calls to guidance, his reward will be equal to that of those who follow him without their reward being diminished in any respect,…” [Muslim]
If they become upright, the problem is solved, but if they remain as they are, then it is not permissible for him to go out with them while they are not wearing Hijaab, as this would mean that he is satisfied with their condition and supporting it and helping them in that.
However, if it is necessary for him to accompany them, such as to protect them from dissolute people who would harrass them, then, in this case, he may go out with them in order to repel or reduce evil.
Allah knows best.