To Lisbeth,I am not an "authority" on this sort of thing, so, my comments are merely what is generally going on here in Idaho concerning this situation.
Concerning your situation --- "Can a sex-offender have children living in his home"!!!
It depends largely upon what type of offense that sex-offender has done. Was it with older kids, or with children, and, it also depends on the rulings of the court of the jurisidction which is involved.
Here where I live (Boise) I have both worked with those bearing the title of "Sex-offender" and live within the same apartment complex with one. Until I knew that either of them were "offenders" I had had absolutely no ideas THAT they were so designated. When I found out, it stunned me completely. The one who lives in the apartment complex where I live, is one of the most OUTSTANDING citizens of this community in virtually all ways.
There is something to take into consideration here in "sex-offender" situations. God forgives ALL sins, excepting Blasphemy against the Holy Spirit, and this forgiving includes those who commit sexual sins. It is people who have placed a NO FORGIVENESS ACKNOWLEDGED on the sin of sex against kids, teens-by-adults, and such.
God does not say that "all sin is forgiveable, excepting the "sex-offender" type as well as the blasphemy against the Holy Spirit" He says "ALL sin is forgiveable, excepting blasphemy against the Holy Spirit" --- so, it is my contentions that THAT MEANS virtually all sins.
In the light of God and rulings for forgiveness, I would say that your situation then, depends on whether or not the "sex-offender" has truly asked God for forgiveness and it has been granted. So, there should be no problems in that case, even though from man's thinking "once an offender, always an offender"! But, if so, then God could also say "once a sinner, always a sinner" and in that case not one of us would get to go through the Pearly Gates.