Her husband’s mother dislikes her – what should she do?

There is no problem that cannot by solved by anyone, as
stated in the question. For every problem there is a solution, but the
problem is not in finding the solution, rather it depends on the one who is
going to implement the solution. Many of those who go through difficult
circumstances and ask for a solution imagine that the person they are asking
is able to take away the problem, but this is not correct. Rather all that a
human being can do is to suggest the best possible ways of reaching the
desired result, but the person must still make the effort to solve his
problem – this is very important and essential. 

With regard to what you asked about: 

Firstly: 

This dislike that they are showing may be based on incorrect
ideas about you, so perhaps it is only temporary and may disappear if you
try hard to be pleasant to them. I say this because we cannot be sure of
what may happen in the future. How often has a girl have been disliked by
her husband’s family in the beginning, then as they got to know her and saw
her good manners and good attitude, they changed their minds about her and
their condemnation turned to praise and their hatred to love. So do not
worry about what may happen, just be cheerful and optimistic about your
future with your husband. 

Secondly: 

You must show your best attitude towards your husband’s
family, who have the right to be treated in a good manner by you because
they are the family of your husband. Pay a great deal of attention to his
parents, and take care of his mother as if she were your own mother. If she
comes to your house, try to meet her with a friendly and smiling face, and
do not pay too much attention to your husband whilst she is there with you,
because this may stir up feelings of jealousy, which are very strong in
human beings. 

Thirdly: 

Turn to Allaah and make du’aa’, and ask Him to help you to
treat them well and to soften their hearts and make them love you. Realize
that no matter how hard you look for a solution, help is ultimately in His
hand. So turn to Him with all sincerity. May Allaah send blessings and peace
upon our Prophet Muhammad and upon his family.