If I have any advice for the OP it would be to concentrate on her own child at the moment:
remember that the fatherhood of your dp is not under doubt, his details are known, one day the other child is very likely to want to contact his half sibling and will be in a position to do so, nobody will be able to stop him
remember that now is your chance to present this situation to your child in a way that he can live with- in 15 years time you will not have that power
remember that one day he will be an adult evaluating his childhood and using that to build on for all future relationships- any loss of trust in you or his father as decent, good, caring people will have terrible repercussions
remember that if he is left to feel that the welfare of his half sibling was sacrificed for him he may carry that burden of guilt all his life
remember that he will think that whatever happens to this child could happen to him if circumstances changed
remember that though he is only little now and no doubt takes his life and family for granted, in no time he will be a pre-teen and, as pre-teens do, he will evaluate the kind of people his parents are to get an idea of the foundations his life are built on
Yes, it is horribly hard for you. But sometimes we do have to do terrible things to protect our children. And paradoxically, the best protection in the present case is openness and acceptance. However much it hurts you.
That doesn't mean that you have to spend time with the other child. But your own child needs to see that you and your dp are behaving like the decent honourable people he needs to believe in. Which primarily means, you need to make sure your dp knows he is to do the decent thing by the child. Because it is his job, not yours. You just need not to stand in his way.