Is tajweed wajib for all people to know? And if our children when reading don’t apply it do we have to punishment them?
There are parts of tajweed which should be applied by all to the best of their abilities, because not applying it changes the word or meaning. This does not mean we punish those who try and cannot, most of all not children. We want them to love the Qur'an and learn it in a pleasant atmosphere and not associate it with pain and punishment. The sin in making a mistake would be on an adult who knowingly and purposefully makes a mistake which changes the letter or makes a mistake which changes the meaning that Allah ta'aalaa meant.
There are two types of mistakes in tajweed, one is the obvious mistake which should be avoided by all, the best we can; the second is hidden mistake, which only those who have knowledge of tajweed recognize and a mistake of this type is not considered sinful. Allah knows best
Please see the following PDF in which the details are given: