URL Rewrite of domain name in IIS 7 - asp.net

Question

I have two asp.net sites in IIS, api.mydomain.com and mobileapi.mydomain.com. and some of the requests to api should be rewritten to mobileapi. I cant get it to work. From my experiments it seems like I cant rewrite the domain name part of the url with rewrite. If I change to redirect everthing works (except that I want a rewrite and not redirect)
However, if I instead redirect to something on the same domain, lets say I swap the action url to /testing/{R:0} (without any domain name) then it works as expected and rewrites just fine.
My web.config
<modules runAllManagedModulesForAllRequests="true">
</modules>
<rewrite>
<rules>
<rule name="Proxy mobile API" stopProcessing="true">
<match url=".*" />
<conditions>
<add input="{REQUEST_URI}" pattern="([^/]+)" />
<add input="{StaticRewrites:{C:0}}" pattern="(.+)" />
<add input="{HTTP_HOST}" pattern="^api.mydomain.se$" />
</conditions>
<action type="Rewrite" url="http://mobileapi.mydomain.se/{R:0}" />
</rule>
</rules>
<rewriteMaps>
<rewriteMap name="StaticRewrites">
<add key="mobile" value=" " />
<add key="scripts" value=" " />
</rewriteMap>
</rewriteMaps>
</rewrite>

Answer 1

Depending on the project type you have setup, but if you are using MVC 4 you can simply make this switch in the Global.asax.cs file.
protected void Application_BeginRequest(){
//mobile device detection and redirection
if (Request.Browser["IsMobileDevice"] == "true"){
Response.Redirect("http://mobileapi.mydomain.se");
}
}