Having typed out a long reply, and then reading some of the responses, the OP could well be a wind-up, or a reverse AIBU, but having typed it, I'll post it anyway:
I'm not sure about this. I think I've read here that if a parent has parental responsibility, then where that parent exercises that parental responsibility is up to them, and the other parent doesn't have the right to refuse contact solely on the grounds that they don't know where that exercising of parental responsibility is taking place.
In this particular case, the father is just as much a parent as the mother is. I doubt any court would permit a mother to refuse contact on the grounds that she doesn't know where her child is when that child is with its father. And I doubt any court would insist that the mother should have the right to meet the stepmother.
Ultimately, and it's also the court's view these days, it's not about the adults (who only have responsibilities, not rights), it's about what is in the best interests of the child. Personally, I would think it would be in the best interests of an 8 year old to know that his mother knows where he is when he is with his father. An 8-year-old, being introduced to his father's new partner, and in a new home, could well find that quite a daunting transition, and some reassurance that his mum knows where he is could help him settle.
So, although I don't think the mother has the right, as such, to your address while the child is with his father, it is in the best interests of the child that there is as little conflict as possible between his parents over their responsibilities and his care. And on that basis, I think you should accede to the mother's request to know the address where you and the child's father live, which is where the boy will usually be when he's with his father.