This second file contains one umlaut in ISO-8859-1 encoding. Without this umlaut there is no problem.

Is the encoding decleared in the "<?XML ... ?>" header? Without it, any XML parser assumes, as it must, that the encoding is in UTF-8. The complete, proper declaration for your case would be like this:

<?xml version="1.0" encoding="ISO-8859-1"?>
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See this for an explanation of this issue in beginners' terms.