Android streaming music from desktop, controlled by another android!
What you need is a software which acts as an UPnP Control Point on your new phone, and a Media Renderer with Push on the old phone. A control point is capable of exactly what you need: browse Media Server (your desktop) in the same way as you do with your old phone currently, but it doesn't play itself, instead it tells the Renderer "hey, start streaming that URL". Then it just observes the Renderer and can control the playback (if Renderer supports being controlled). That "being controlled" part is called "Media Push": instead of browsing the Server from Renderer directly, the Controller tells the Renderer what to do.

Finding a Control Point for Android should be easy (i won't present any suggestions, just google "Android UPnP Control Point"). There is a solid chance that iMediaShare is a Control Point already. But i am afraid that Renderer with Push for Android is hard to find. It essentialy means that the phone must sit on the network with opened server socket, doing nothing, waiting for commands. And that's perhaps problematic with Android. I already answered one question here on a similar matter and the asker didn't report any conclusion. You are welcome to pioneer the search for such Android app :-)