Checkout this answer...
I've tried this and it works well
How to open desktop site in webview in android
You can set user agent for your webView programmatically
In case something happens to the link, here's the answer for your question from that link:
private static final String DESKTOP_USER_AGENT = "Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/37.0.2049.0 Safari/537.36";
private static final String MOBILE_USER_AGENT = "Mozilla/5.0 (Linux; U; Android 4.4; en-us; Nexus 4 Build/JOP24G) AppleWebKit/534.30 (KHTML, like Gecko) Version/4.0 Mobile Safari/534.30";
//Choose Mobile/Desktop client.
WebSettings settings = mWebView.getSettings();
settings.setUserAgentString(DESKTOP_USER_AGENT);