Praise be to Allah (The Glorified and Exalted).
The Importance of the Husband/Father:
The foundation of society is a family composed of a husband and wife. The Prophet (peace and blessings of Allah be upon him) had once said that he would have told the family to fall in prostration before the father, if that had been permitted by Allah (The Glorified). This statement alludes to the great importance of the role of the husband/father to the family. Especially that of the biological father. Children view step-fathers as more of outsiders and strangers, unless they treat them better than the biological father. However, if the biological was friendly with his children, then his position will always be higher.
The children require the father for his authority and guidance in their lives. Further more, the male children require a father to look upon as their male role-model, for male companionship, to set a standard of behavior for them to follow. Not to mention, to play sports with, etc. The female children require a father to provide them the male acceptance they seek and to set a model of behavior and attitude that they should seek for in a future husband.
When the father is missing, then it is no surprise that you find these types of families in which the children are running wild. One cannot be surprised to see the male children become nonreligious and accepting the male view of manhood coming from their fellow peers (in your situation mostly non-Muslims) and television actors, that engage in all forms of abomination. The female children also become misled in life and nonreligious, at an older age, running around trying to seek male acceptance and approval from the "wrong type" of man, destroying their own lives. It is also the case that in the mind of a child completeness of a family is viewed as having both mother and father.
Step-Father?:
You are living in a land in which there are not many Muslims. Getting a divorce will be devastating to you, because you will enter into an abyss of the unknown. Your husband is already a Muslim and the biological father to your children. And you have mentioned before that he treats you well. If you were to get a divorce, who knows if you will every find another Muslim man to marry you or to take care of your children. You will lose your male partner and father to your children. Considering that most men do not like to look after the children of other men, especially in your land in which when the children reach their teenage years, they become a bit more troublesome to deal with. That may lead to trouble in the relationship with the new husband, when the children of your previous husband to do not behave well. It is also the case that in your land, it is honestly difficult to find good Muslim men that are religious and have the same mentality as you. Because many of them come from immigrant families with different cultural practices and ideas about marriage. You may end up not every getting married again, because many immigrant parents do not wish for their sons to marry outside their culture or race, so no male partner or father to your children, or you may get involved in a worse marriage. Many Muslims in your land are not very knowledgeable about Islam to begin with. It is better for you and your husband, sharing the same mentality and culture and idea concerning marriage, to start learning Islam from scratch and teach it to your children, free from any cultural practices found in Central Asia or the Middle-East.
What to do about the Parties:
If you and your husband can financially afford to, then move into your own home. If your husband can still help his mother, then fine. If not, then that is life, she will lose her home to the bank. However, you can allow her to come and live with you and your husband. This way, you set the rules, no alcohol in the home and no parties, and get rid of the other woman. Be patient with your husband, especially if they have some emotional attachment to the home. You may try to influence him when you are alone with him by behaving nicely and speaking kindly to him, smiling, reminding him of religious duties, etc. This way when his heart is softened, he may act and realize that this situation is not good to provide an Islamic life for one's family.
In the meantime, during these parties, you can isolate your children into a room alone with them and tell them stories of the Prophets (peace be upon them) and tell them about the Angels, description of Heaven, etc. When you pray, try to do it together as a family with your husband and children and let the kids mimic your movements, etc. Push the children into the religion a bit more strongly and if they see the people at the parties, just tell them kindly that people live their lives differently and that is not part of their life and they can never join in that, because it is against what Allah (The Exalted) wants. And remind them of the story of Adam (peace be upon him) and his downfall, by disobeying Allah (The Exalted). Children at their age will understand that.
Emigration:
Eventually, when your children pass the elementary school level, I believe it would be best to move into a city with a more significant Muslim population. So that your family can pray at the masjid (mosque), your children may attend an Islamic private school, make friends with Muslim children, you can have Muslim friends, eat halaal food, etc. If you are studying something in the medical field (nursing, doctor, etc) there is also a chance to move to a Muslim populated nation such as Saudi Arabia, because they hire many foreigners in this field, and there are also teaching jobs available, such as teaching English, or engineering work, etc. If you want to eventually move to a Muslim populated nation such as Arabia, then look in that matter by searching "google" for Saudi jobs.
Some Links to Help you Teach your Children and Learn about Islam:
1) Proving Islam:
http://www.turntoislam.com/forum/showthread.php?t=40837
2) Islamic files:
http://www.turntoislam.com/forum/showthread.php?t=65248
3) In your land many people believe in evolution, you should teach your children the falseness of this belief when they are at an older age, teenagers, bookmark the site or save some of its information on a word file. Science Against Evolution:
http://www.turntoislam.com/forum/showthread.php?t=62132
4)
http://www.islamreligion.com/
5) Allow your children to sit on your lap and watch this show with them. This will also psychologically allow them to make a connection with the religion of Islam and their own identity as americans, especially important when they get older, because the host of the show is an american man. This way they do not view the religion as foreign to themselves, but accept it as also being part of their identity. The Deen Show:
http://thedeenshow.com/
6) Because you live in a land with many christians. And unfortunately, some of them that are hostile to Islam, as your children get older, teach them the falseness of that religion by the lectures with former christians on the Deen Show and articles from the following site:
http://www.answering-christianity.com/ac.htm
And Allah Knows Best.