I don’t use any such plugins myself to suggest one unfortunately but i can see why that plugin causes problems, the scripts and styles are just printed outright rather than utilizing the WordPress enqueue system. If the author updated his code to correctly enqueue the scripts or styles he needs it would not be creating any conflict with Post UI Tabs.
You can use as many plugins are you want alongside each other in theory, providing they are coded well and correctly using WordPress conventions(such as the enqueue system, as but one example).
What kind of features do you need from an audio player? Is there something in particular it has that you want from such a plugin? Knowing more about your requirements(or desires) may help suggest another plugin.
Maybe you could have a browse through the available plugins and give a few of them a test run…
https://www.ads-software.com/plugins/search.php?q=mp3+player