If I use one of this two properties everything works fine but simultaneously these two properties do not work. Is there any way to do the same?
It's not a normal behavior. There is no conflict between binding to Visibility property and setting text in resource file. Have you set DataContext for your Binding?
Please see the following code sample, it worked well.

<Grid>
<TextBlock x:Uid="txtControldName" Visibility="{Binding IsMyControlVisible}"></TextBlock>
<Button Content="test" Click="Button_Click"></Button>
</Grid>
public sealed partial class MainPage : Page,INotifyPropertyChanged
{
private Visibility _IsMyControlVisible;
public Visibility IsMyControlVisible
{
get { return _IsMyControlVisible; }
set
{
_IsMyControlVisible = value;
RaisePropertyChange("IsMyControlVisible");
}
}
public MainPage()
{
this.InitializeComponent();
this.DataContext = this;
}
public event PropertyChangedEventHandler PropertyChanged;
private void RaisePropertyChange(String PropertyName)
{
if (PropertyChanged != null)
{
PropertyChanged(this,new PropertyChangedEventArgs(PropertyName));
}
}
private void Button_Click(object sender, RoutedEventArgs e)
{
IsMyControlVisible = IsMyControlVisible == Visibility.Collapsed ? Visibility.Visible : Visibility.Collapsed;
}
}
Please note that you need to implement the INotifyPropertyChanged interface, when the property value is change, it will notify the UI.