I am sorry to hear your repair is turning into a desaster!
Whereas I fully agree that they made a mistake by sending you a wrong pair (how exactly did u know its someone else btw were they broken?) it is a very common procedure in retail to do what they offer you now: for them to be ALLOWED to send you ANOTHER pair (which means technically you could keep both and disappear - not saying you are, just technically) they, in return, NEED to know you are sending the other ones back which means they either need the tracking number for the parcel adressed to them or, for high value items, the entire thing back on their desk before they send the other one out to you.
While I understand that this may seem frustrating for you, i want to assure you the procedure itself is totally okay. Just imagine it were a flap bag sent for repair - they cant let you keep a wrong one they sent and send ANOTHER one out, hoping you will be nice enough to return the wrongly send one. you would not BELIEVE the things customers do - it doesnt matter if they are chanel ones or H&M. Ive worked in retail for a year... and if you were loosing your patience and telling them "im not sendint it back till i get my own" - if the lady had a bad day (or wasnt experienced..) she could be twice es worried now, quite understandably, that your not gonna send it back at all because you are so pissed off

you know what I mean?
bottom line: nobdoy should hang up on you. nobody should be rude, you are to be treated politely and nice at all times. yet, nobody is holding your earrings hostage - its a standard procedure to return product A before B is send out. If you want to give it one last shot why dont you suggest that while you understand that they need their earrings back, you also want to be sure that you dont send them back and end up with none at all (which i think is the bottom of this, right?) . therefore if they could please send you a written email stating that there will be an exchange of product: you send theirs back, in return you get your own ASAP. written documented like that you are in safe hands - better than just an over the phone promise.