LODGER OR TENANT?

Tenancy Deposits

My daughter allowed a friend of hers and her young daughter to occupy 2 rooms in her house (which we own). We gave permission in writing for this and confirmed she was our daughter's lodger in writing. My daughter pays no rent so rather than her pay her direct the lodger paid her rent to us fortnightly. She proved to be the lodger from hell and following several warnings was given one week's notice to leave (reasonable notice under the circumstances). She has now taken advice and refuses to leave (her stuff is all over the house). Her advisors say she is technically a tenant as she paid rent directly to us and we have to give 2 months' notice.. is this correct. (I have e mailed the helpdesk but have had no reply)