All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we would like to establish that those children have the right to visit their father, but at the same time he is obliged to fulfill his duties towards you, and he should not let the presence of those children prevent him from fulfilling those duties. In addition, he is obliged to protect you and your children in particular from their harm.
The best advice we can offer you is to adhere to patience and endure the misconduct of these children and the possible neglect of your rights on part of your husband; this would hopefully strengthen the bond between you and your husband and you may thereby gain in your marriage much more than what you lose on the weekends during their visits.
You should try to reach a mutual understanding with your husband and not consider asking for divorce. Marriage in Islam is a sacred bond, which the spouses are enjoined to preserve. It is described in the Quran as a solemn covenant. Allaah The Exalted says (what means): {And how could you take it while you have gone in unto each other and they have taken from you a solemn covenant?} [Quran 4:21]
Why don't you seek the reward from Allaah by working with your husband to plan an educational program that could improve their manners instead of leaving them prey to alien un-Islamic cultures? In this way, you would prevent some of the harm that may befall your family from of their visits.
In brief, we advise you not to consider divorce, which would destroy your family, because Islam came to build not to destroy. It seeks to unite people in goodness, not to divide them. Therefore, stern warnings were given to the wife who demands divorce for no valid reason. Thawbaan narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: "If any woman asks her husband for divorce without a valid reason, the scent of Paradise will be forbidden to her." [Abu Daawood, An-Nasaa'i, At-Tirmithi and Ibn Maajah]
It is impermissible for you to ask for divorce except for one of the valid reasons for divorce that have been previously mentioned in Fatwa 131953. Also, spouses should not opt for divorce even if there is a valid reason unless it becomes obvious that the benefits achieved outweigh the evils incurred by it. Needless to say, divorce is not be the optimal solution in all cases.
Allaah Knows best.