Load stylesheet for "rem" value fallback to "px"
I have tested the following code in IE8 and Safari and it works, although I cannot test on the Galaxy Note or Opera Mini. The following javascript allows you to test rem support. Since IE9 or lower throws an error when you try to set as rem, I used a try{}catch(){} - newer browsers should remove the value as soon as its set when they don't support setting the value as such. I don't know if this solves all your problems (if the Galaxy allows you to set rem but doesn't apply it, then this won't work). I have used pure javascript, so you don't need support for anything else (like jQuery).
function supports(attribute, test){

    var supports = false;

    try {
        var div     = document.createElement(&quot;div&quot;);
    
        div.style[attribute] = test;
    
        if(div.style[attribute] === test){
            supports = true;
        }
    } catch(e){}

    return supports;
}

You could then test for rem support as such:
if(supports(&quot;fontSize&quot;, &quot;1rem&quot;)){
    /* Rem supported, don't add your stylesheet */
} else {
    /* No rem support, add another stylesheet to make up for it */
}

This is a purer and simpler, and more reusable, version of your code. Sniffing user agents is generally a bad idea as they inevitably lead to confusion, and a user agent string in the future might match what you are testing for and therefore have an unexpected outcome. It is also best practise to allow for more universal solutions. You could, for example, use this same function to see if you can set background-imageto 1rem and it would return false.
Update
I have just done some testing with browser stack (which, granted, is an emulator) and the Galaxy Note 2 does support rem. And not because my function says it, I made a page with this code:
&lt;!DOCTYPE html&gt;
&lt;html style=&quot;font-size: 12px;&quot;&gt;
&lt;head&gt;&lt;/head&gt;
&lt;body&gt;
    &lt;div style=&quot;font-size: 5em;&quot;&gt;5EM
        &lt;div style=&quot;font-size: 2em; font-size: 2rem;&quot;&gt;2(*5)EM/2REM&lt;/div&gt;
    &lt;/div&gt;
&lt;/body&gt;
&lt;/html&gt;

and the nested 2(*5)EM/2REMis smaller than the 5EM, which indicates its getting the base value from the html tag and not from the parent, indicating rem support.