Okay, bear with me here. I promise I'm not trying to be a jerk, but I still think there is some confusion with what you're attempting. Your 1st file, 'edit-themes.php', seems like it works the way you want it to. It has a text box that has a default value "../content/themes/". I'm not sure why you want that, but whatever.
The second file, 'themes-updater.php' still has me confused. You get the submitted value of update_theme_url from the form, storing that in $update_theme_url. Then you store it again in $url. By the way, the quotation marks in this line have no net effect in this case (there's string interpolation, but it ends up the same):
$url = "$update_theme_url";
At that point, if you just submit the form from 'edit-themes.php', the value stored in $url is "../content/themes/". I don't understand what you're trying to do with that.
Here's where things get really weird:
$fh = fopen("../theme-loader.php","r");
That opens a file, theme-loader.php, in read only mode. And then with the following line:
fwrite($fh,'$update_theme_url');
you are trying to write to it? Okay, so what is it you want? Are you trying to store the $url value to a file? Or are you simply trying to pass the value of $url to another php script?
It would be helpful if you would write out what you're trying to do. Something like:
1. Allow the user to select a theme from a select box on a form.
2. Submit the form.
3. Store the selected theme as a value in a flat text file.
4. Forward the user to an index page with the selected theme applied.
If you do that, you'll get some better answers on here. I have a feeling that you're using fwrite for something that it doesn't actually do, but I can't be sure.
Good luck, I'm going to be away from the computer for a while but I'll help if I can. Maybe someone else will step in.