This thread moves too quickly for me to keep up with fully, so I might be off track with this. It is reported that DN was living under a bridge at the time the crime happened and I have seen posts here of people wondering how this can be determined. The following thoughts are based on my knowledge of working in child protection in the UK. I would imagine the same / similar would apply in the US?
Given his convictions and background (sex offences, violence, domestic violence), DN would be considered a risk to children. People who are a risk to children should not be living with children. Child protection services would be alerted by the police / prisons / probation if an offender was known to have contact with children. The other parent would likely be given the ultimatum of if you continue living with this offender then your children will be removed from your care. So, when he went to register as per his SO order, if DN gave his address as living with KN, they would be obliged to inform childrens services, which could lead to them removing the children. DN could perhaps have said he was homeless to prevent this from happening.
I have know idea where KN was living at this time, and have no idea if this would be anywhere near Delphi. I know we cant comment on that here anyway, but just throwing this thought in here!