Joanna Fortune: How can I prepare my children to meet their dad's new partner?

It is worth noting that children will often choose to discuss changes with their other parent (you in this instance), and as such, if he can let you know what he has said to them and how, then you can mirror the message so your children are hearing a clear and consistent message from you both.
He may feel that he doesn’t need to discuss his relationship with you or the decision to live with his partner, which is reasonable. However, he does need to discuss the children you share and how any such decisions may affect them.