What the wife is obliged to do is to obey her husband; he is the one whom she is obliged to obey. If the husband agrees that she may visit her family, it does not matter if his parents do not approve. 

But a woman should strive to please her husband’s parents and treat them in a manner that is better, and not confront them. This will have a great effect on giving stability to her life with her husband. 

You should understand that your husband’s parents may make things difficult for you because they think that you have taken away the one who is most dear to them. So you should handle this matter wisely and not be the cause of arguments or division between your husband and his parents. Rather you should try to help your husband obey and honour his parents, and you will find the effects of that, in sha Allah, in your own children [i.e., they will honour you in turn]. 

You have to treat them kindly, because kindness is never to be found in a thing but it beautifies it, and it is never lacking in a thing but it makes it ugly. If you see that they are treating you badly, then remember the words of Allah (interpretation of the meaning): 

“Repel (the evil) with one which is better (i.e. Allah orders the faithful believers to be patient at the time of anger, and to excuse those who treat them badly) then verily he, between whom and you there was enmity, (will become) as though he was a close friend”

[Fussilat 41:34] 

For more information, please see al-Mughni, 7/225 

And Allah knows best.