In the name of God, the Most Loving, the Most Merciful
Below are several things you need to consider
1) If he converts to Islam only to marry a muslim woman, will he still continue with his previous habit such as drinking. Can you reach an agreement with him that every time he drinks, he will leave the house, he will never be too drunk that he will beat you and can you avoid your children from seeing their father drinking alcohol?
2) If you tell your children to pray , to wash their private part after they answer the call of nature, or for many other islamic rules and they refuse, are you sure your husband will not defend your children instead of you?
3) If you tell your children not to go out on a date except accompanied with friends or relatives or be alone in a closed room with a non-relative males, will your husband agree with it since it might be part of his culture and thus he does not see any danger in it that the daughter might end up in a prostitution ring?
4) Will he have a problem with you or your daughter wearing the headscarf?
5) If you tell your children not to shake hands or hug the opposite gender because sometimes it can bring temptation , will your husband agree with it?
6) He might not be against Islam but his friends and relatives might call you terrorist when they have the chance.
7) Because non-muslim men can get sex free of charge without marriage and dump their girlfriend without protection from the court, why should they pay dowry to be in a marriage? pay compensation if they divorce? and be burdened with all of the responsibility of Islamic marriage ?
8) If there is a divorce in Islamic marriage a man is responsible 100% for providing the financial aspect of the children. While in many non-muslim countries this responsibility is shared 50/50. Do you think you have the money to provide for your children even 50%? Even if there is no divorce you simply must share 50/50 for your rent , your food and your children no matter how low your salary is. If you don't want to work to focus on your babies, you just have to accept the humiliation of not able to provide for yourself even though you are already 40.
9) If he decides Islam is not for him, or does not agree with you telling the child not to play around with girls/boys, and divorce you, you already wasted more than 10 years of your life with him. A woman is only attractive before menopause and majority of men prefer a 22 year old lady than a 42 year old divorcee. While for a man they only need to have a lot of money to get a lady, a woman have it a lot tougher to find another partner as she gets older.
Then again my husband is a Muslim convert. He is interested to learn about Islam. So do istikharah prayer and may Allah protect you if you wish to enter into this kind of marriage.