Wiping over the headcover (khimar) when there is a piece of cloth (headband) under it
Question

If I follow the view of the Hanbalis about it being permissible to wipe over the headcover that is wrapped under the chin, should I be wearing the headcover directly on my head, or is there nothing wrong with that [wearing a headband and the like]? Because I wear a small cloth (kerchief or headband) under it that goes around the head only, and does not go over the ears or under the chin. Is it sufficient to wipe the headscarf only, and not this piece of cloth?
Praise be to Allah.It is proven that the Prophet (blessings and peace of Allah be upon him) wiped over his turban when doing wudu.
It was narrated from Ja‘far ibn ‘Amr ibn Umayyah that his father said: I saw the Prophet (blessings and peace of Allah be upon him) wiping over his turban and khuffs. Narrated by al-Bukhari (205).
It was narrated by Ka‘b ibn ‘Ujrah, from Bilal, that the Messenger of Allah (blessings and peace of Allah be upon him) wiped over his khuffs and headcover. Narrated by Muslim (275).
Al-Nawawi (may Allah have mercy on him) said:
What is meant by the headcover here is the turban, because it covers the head. End quote from Sharh Sahih Muslim (3/174).
By analogy with that, it is permissible for a woman to wipe over her headcover, especially that which goes under the chin. Whatever is prescribed for men is, in principle, also prescribed for women.
Moreover, the reason is the same, which is to alleviate the difficulty of taking it off and putting it back on again. In fact, women’s need to wipe over their headcovers is often more obvious and greater than that of men, as is quite clear.
Al-Hasan narrated from his mother, from Umm Salamah, that she used to wipe over her headcover.
Narrated by Ibn Abi Shaybah in al-Musannaf (224).
For more information and to see the views of scholars regarding this matter, please see the answer to question no. 148129 .
Secondly:
In order for it to be valid to wipe over the headcover, there is no stipulation that the headcover should rest directly on the head, because there is no text to that effect. Rather it is sufficient for it to cover the head as socks or khuffs cover the feet, and it is permissible to wipe over them even if there is another pair of socks or khuffs under them. This is the view of the majority of scholars.
Ibn Qudamah (may Allah have mercy on him) said: If he put the outer khuff on before invalidating his wudu, it is permissible to wipe over it in all cases, whether the inner one is intact or has holes. This is the view of al-Hasan ibn Salih, ath-Thawri, al-Awza‘i and ashab al-ra’y. Malik disallowed that in one of the two reports narrated from him, as did ash-Shafa‘i in one of his two views, because usually there is no need to wear the second khuff, so there is no need for a general concession regarding it, as is the case regarding a plaster cast.
In our view, however, if the two khuffs together are covering the foot and it is possible to walk in them, then they are like one khuff, even if the inner khuff has holes. His saying that there is no need for it is not correct, for if the land is cold, it is usually not sufficient to wear just one khuff."(Al-Mughni  1/364).
And Allah knows best.