You don't have to be a citizen to receive resident tuition. However, you do need to have been resident in the UK for at least 3 years AND hold permanent residence in order to receive it.
Just to add, you can receive eligibility for home fees if you are a EEA or Swiss national. Meaning that you have been resident (for three years) and a citizen of one of the following countries: Austria, Belgium, Bulgaria, Republic of Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden and the United Kingdom.
Iceland, Liechtenstein and Norway are EEA member states, but they are not members of the European Union (EU). Swiss nationals are not EEA nationals, are not EU citizens, but they qualify for home fees.
To qualify for home fees, your daughter would have to be 'ordinarily resident' in the UK.
Look on
http://www.ukcosa.org.uk/student/fees_student_support.php for more information about qualifying for home fees and whether or not you have to pay international fees.