بِسْمِ اللهِ الرَّحْمنِ الرَّحِيمِ
Whoever teaches the reading of the Quran to his son (without memorizing it), all his sins, whether previous or subsequent, will be forgiven. And whoever makes his child memorize the Quran, will be raised on the Day of Judgement in the appearance of a full moon; and his son will be asked to start reciting, and for every ayat read by the child, the status of the parent will be raised to the next higher grade of Jannat, till the recitation of the Quran is completed.
Conversely if you deprive your child of knowledge (of religion) for the sake of a few dollars, not only will you be deprived of eternal reward, but you will be held accountable before Allah. Are you depriving your child of reading the Quran for fear that after memorizing the Quran they will be dependent on others for their living?
Please remember that not only do you expose your children to eternal misery, but you carry a very heavy accountability. A hadith says
"Each one of you is a guardian, and will be questioned about those under his control."
Everyone will be questioned about his subordinates and dependents as to what extent he taught them. As a proverb says, " Should one discard clothes for fear of lice?"
If you share religious education to your child, you will be free from your responsibility.
As long as the child lives whatever good deeds he does, whatever salat he performs, and forgiveness that he seeks from Allah for you will elevate your position in Jannah. If for the sake of this life and for a few dollars you keep him ignorant of deen, not only will you have to suffer for this misdeed but whatever evil and misdeeds he does, your account will not be free from this burden. For God's sake have pity on yourselves. This life in only a passing phase and death will put and end to all its hardships, however great, but the sufferings for which there is no end will be everlasting.
At the end of the day Allah will provide for you if you have faith in him. Your child can be a hafiz and have a worldly education as well.
Sayyidina Abdullah Ibn Masood R.A. relates that I heard
Rasulullah (صلى الله عليه وسلم) say " The one who reads Suratul Waaqiah every night, poverty will not befall him. (Abu-Yala, Baihaqi)
Don't sell your self out for a couple of bucks. The money wont last but the suffering or joy in the hereafter will.
Make your choice.
* Note* Some of this is an excerpt from Faza'il e A'maal