All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
Children should be gently forbidden from committing bad actions to discipline them, even if they are below the age of competence for religious assignments. Abu Hurayrah narrated that Al-Hasan ibn ʻAli took a date from the dates of sadaqah (charity) and put it in his mouth. The Prophet said (to him) in Persian, "Kakh, Kakh! (i.e. Do not do that) You know that we do not eat what is given in charity." [Al-Bukhari and Muslim]
ʻUmar ibn Abi Salamah said, "I was a boy under the care of the Messenger of Allaah and my hand used to go around the dish while I was eating. So the Messenger of Allaah said to me, 'O boy! Mention the Name of Allaah and eat with your right hand, and eat of the dish what is nearer to you.'" [Al-Bukhari and Muslim]
Some scholars held that it is recommended to discipline young children, and some others deemed it obligatory. Some scholars held that it is obligatory on the parents in particular. As-Saffaareeni wrote:
"Al-Hajjaawi stated that it is recommended to forbid young children who have not reached puberty from prohibited acts, males or females, as part of disciplining and educating them. The Hanbalis asserted that the individual who is incompetent for religious assignments is not to be forbidden from committing prohibited acts except for the purpose of discipline and admonishment. The apparent indication of the statement of Imaam Ibn Al-Jawzi in this regard is that it is an obligation to forbid the child (from evil). His statement, 'He must throw his (the child's) wine away and forbid him from drinking it and must also forbid him from committing fornication...' clearly indicates the obligation..." [Ghithaa' Al-Albaab]
Hence, based on the scholarly view that it is obligatory, you would bear a sin for refraining from forbidding them; whereas based on the view that it is only recommended, you bear no sin for it. However, it is worthier of the parents to bear this duty, especially given that some scholars deemed it obligatory on them to forbid their young children from committing prohibited acts.
The Kuwaiti Encyclopedia of Islamic Jurisprudence reads, "Ar-Raafiʻi reported the obligation of fathers and mothers in this regard, and this view was declared correct by An-Nawawi, as evidenced by the verse that reads (what means): {O you who have believed, protect yourselves and your families from a Fire ...} [Quran 66:6] ʻAli ibn Abi Taalib Mujaahid and Qataadah interpreted the verse to mean, 'Teach them what helps them escape Hellfire.' This meaning is clear in the apparent indication of the verse..."
If the parents fail to forbid their young children from committing prohibited acts, then such children should still be advised by others. This duty should not be neglected merely to avoid potential debate with their parents or the possibility that these children might get confused because of the conflicting opinions. On the contrary, they may benefit of the advice in their future.
We would like to point out that the parents of these children are more in need of advice and direction, especially since you have mentioned that they commit prohibited acts that are quite sinful and may lead to disbelief. Please refer to fataawa 53349 and 16844 about the best ways of calling relatives who have a lax commitment to Islam to return to the straight path.
Allaah knows best.