Our Jack Russel Terrier, Champ, was not very happy when we brought home the new addition, a Toy Fox Terrier, Maximus. For a while there, Champ doesn't have to do anything with Max. We slowly work on it and told Champ that he would be his buddy from now on.
A couple of days ago, my wife saw Champ in his chair so she put Max there too. Champ was ignoring him at first. Max made his way to be closer to him.
He gets uneasy when Max touches his ball or uses his chair. I think that the rivalry will soon vanish. Champ needs a little more time to get fully acquainted with Max.