Use redirect_to
in your destroy action:
# assuming this is a nested resourceful route like: /parents/:parent_id/children/:id
def destroy
parent = SomeModel.find params[:parent_id]
child = parent.children.find params[:id]
child.destroy
redirect_to :back # will redirect back to the referrer (page from where you came from)
end
What that does is essentially: redirect_to request.referrer
which will take the user to the page they were on when they clicked delete on the child model.