class MyClass
{
    CultureInfo currentCultureInfo;
    public MyClass()
    {
        //defaulting to en-US
        currentCultureInfo = new CultureInfo("en-US");
    }

    public void SetLanguageToEnglish()
    {
        currentCultureInfo = new CultureInfo("en-US");
    }

    public void SetLanguageToItalian()
    {
        currentCultureInfo = new CultureInfo("it-IT");
    }

    public string GetTranslation(string s)
    {
        //By the way, you should to the same to 'a' and 'rm', since they don't need to be instantiated each time. But I'll use your code to avoid confusion.
        Assembly a = Assembly.Load("read_display");
        ResourceManager rm = new ResourceManager("read_display.language.languageRes", a);
        return rm.GetString(s, currentCultureInfo);
    }
}