Hi, I've been through a lot of family problems too.
Had family problems similar to yours.
If I am perfectly honest, I'd say that your partner should see his 2 daughters.
because from their point of view, they need a Dad.
And as they grow up, they will wonder where their father is.
Even if it is for a couple of hours, once every month.
Maybe your partner should see them, just his daughters though, in a public place, like a park or something.
Just arrange a time and place, you stay at home with you little boy, and your partner doesn't have to have any contact with the girls' mother.
Your little boy doesn't need to know aobut them or see them untill maybe he's older and will understand things.
I just know what it's like having your father reject you, becuase of your mother.
if things don't work, leave it a while, and have a good think about things.