are you taking her on walks, active walks that tire her out? my experience has been that bored, worker breed animals get territorial and snippy when they aren't keep active. she does sound like a child who is afraid they aren't loved so pushes any competition aside. i like the idea of also getting the two of them playing together with you. When you make decision, think of what breeds are dominate in her and whether you have taken that into consideration when you work with her.