i would say review and discuss the situation every 3 months with no verbal comitment as to it neccesarily changing.
after 3 months you may need to go down the court route if he pushes it, but that will give you time to prepare.
you may want to ask some following questions.
how old are ow other children?
what would sleeping arrangements be?
no alchohol or drugs with dd around ever!
supervised (by you) contact for at least 3 months, then open to disussion of supervised by another trusted person or contact centre when you are sure depression, drugs and alchohol are not going to impact on dds care and development.
discuss dd possibly meeting ow and her children, after maybe 6 months and then 3 months after that disuss further contact changing. this will give evry one a chance to see if ow will remain a stable figure in the life of dd and H.
this does not need to be a ridged time frame but gives you a possible plan to put to H.
if he is not happy then he can contest it if he choses through a solicitor. But I would be sure to come across as strong reasonable and putting dd first.
I would sugest he can see dd at least once a week two times if you can bear it. that way you are not standing his way of maintaing a relationship with her.