First of all, there is no such thing as a Christian who doesn't really believe. You're not a Christian.
Secondly, if you were even a Christian, you never should have married a Muslim, but then, you are faithless. You're not a Christian. 2 Cor 6:14 clearly says "Do not be unequally yoked with unbelievers. For what partnership has righteousness with unrighteousness?"
Your faith is a responsibility. You have become a bridge between heaven and earth to manifest the purpose and glory of God - paramount among these is to raise godly children. Look what God said about Abraham.
For I know him, that he will command his children and his household after him, and they shall keep the way of the LORD, to do justice and judgment.
- Gen 18:19
Because you are neither here nor there, with no solid footing in Christ, it was easy to lose your kids to Islam to a woman that truly believes in Allah. She has faith and your faithless. Look what Joshua said:
And if it seem evil unto you to serve the LORD, choose you this day whom ye will serve; but as for me and my house, we will serve the Lord.
- Jos 24:15
You are supposed to be the spiritual head of your family and you're doing a horrible job at it. You don't believe in anything, and you married a woman that has faith. She is doing right by teaching faith to your kids. In a healthy home, couples are supposed to be of one faith so they can jointly teach the kids the ways of their god, and to be decent and godly people. That you're called weak is irrelevant to me. I hope you eventually come to the true knowledge of christ and to the power of his resurrection.