Sorry - the whole thing sounds a mess.
Your Ex and his Ex are friends.
You and Ex had a violent relationship.
Your Ex has convictions for what? Sexual abuse against children?
You have a verbal agreement with SS- means nothing.
SS interviewed her and did nothing - if they were that concerned about this man and another child was involved - they would have done something. How do you know he slept over at her house and how do you know that SS advised her not to?
Ex has wanted you to have ONs and you and your DP refused. because it is not convenient , because your new child was more important. Not a good signal. DH and your DSD has been seeing each other for 18 months, when was it going to be convenient to introduce your daughter to her sister. On your calculations you were in her life for 3 yrs.
The EX is now refusing ONs, because she is not allowed to know where her daughter is and you are alleging a safeguarding issue. Bloody sensible mother.
Your DP needs to take both his children to a place of safety and allow them to get to know each other - how the 6 yr old is going to cope with knowing she has not been seeing DAddy but in the mean time Daddy has a baby who will demand all his attention - the poor kid.
Sorry you and your DP have messed up big style and his DD needs to become a priority in your family -not a when it is convenient we will do x and y but on our terms etc. At 6 she will know her own address, it will take a few visits and she will know her Dads address.
Reality check here. Your poor DSD