From these facts, your ex has a long history of sexual abuse on minors. He is a registered sex offender and also molested his own child. On these facts, I would believe that the court would want him to have monitored visits or no visits at all.
You have an information need at this point. Specifically, you need to see the orders re his sentence. Generally, they include restrictions on being with minors.
The environment you describe is not remotely what I would call safe or suitable for an adult, let alone a minor.
There is no way to relaay answer the question as it requires one to read the mind of a judge.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
If DCFS hasn't already taken the children and placed them elsewhere. You need to get them involved. You also need to get full custody, which given the facts you provided, most like will.
Maryam Atighechi is a family law, real estate and civil litigation attorney in Sherman Oaks, CA. 818-647-1152. Please be advised that although Ms. Atighechi is an attorney, the comments posted does not constitute legal advice. You should not rely on any advice or suggestions written and seek outside, independent counsel. An attorney-client relationship has not formed by reading the post.