His wife does not want to wear hijaab and he fears for his young daughter

Strong
faith must have effects which can be seen in a person’s appearance and
conduct. If a person persists in sin, this is a sign of weak faith.

 What
you have to do is try to plant the seeds of faith in her heart and help it
to grow strong. What is meant by that is the kind of faith that will
motivate a person to behave in accordance with the sharee’ah. Then try
to instill in her a love of the hijaab and of righteous deeds, such as
explaining the benefits of hijaab and how good it is, and giving her books
and audio tapes, if these are available, which speak about that. One of
the most important means which will help to achieve this is to put her in
touch – in an indirect manner – with righteous women who wear the
hijaab and try to have frequent family gatherings with righteous
relatives.

If
you do this, you will have tried various means of convincing her. Then you
will have to oblige her in an appropriate fashion and not allow her to go
out to public places without hijaab. (It is important to explain to your
daughter that hijaab is obligatory and tell her about Allaah’s ruling on
hijaab, even if she realizes that her mother is falling short. You have to
explain it to her at a level that she can understand so that she will see
that there is a difference between the rulings of sharee’ah and the way
her mother is behaving. Who knows – perhaps she will advise her mother,
in the moving and innocent manner of children – to wear hijaab).

 With
regard to the second question, there is no doubt that fathers are
responsible if their wives and daughters do not wear hijaab and do not
adhere to the rulings of sharee’ah, as Allaah says (interpretation of
the meaning):

“O
you who believe! Ward off yourselves and your families against a Fire
(Hell) whose fuel is men and stones” [al-Tahreem 66:6]

And as the
Prophet
(peace and blessings of Allaah be upon him) said:

“Each of you
is a shepherd and is responsible for his flock… the man is a shepherd
over the members of his household and is responsible for his flock…”

But if a person
does all that he can and strives his utmost, but does not achieve any
results, Allaah will excuse him and will not punish him; on the contrary,
He will reward him for his efforts, and Allaah does not cause the reward
for any good deed to be lost.