There is a problem, using a SplitApp in a App.
The App needs to be filled with pages, not with a SplitApp. You probably can create a page, set the SplitApp as her content and add it to the App. But believe me, it doesn't look good.
The only solution you have is to disable the App and enable the SplitApp.
I'm doing this with two div-containers:
<body class="sapUiBody" id="content" onload="init()">
<div id="content_app"></div>
<div id="content_splitapp"></div>
</body>
and control the display elemnt if I want to show the SplitApp:
document.getElementById('content_app').style.display = 'none';
document.getElementById('content_splitapp').style.display = 'inline';
splitApp.placeAt("content_splitapp");
or if I want to go back to the App:
document.getElementById('content_splitapp').style.display = 'none';
document.getElementById('content_app').style.display = 'block';
Hope this helps you