The expected interpretation of "I want her home" in the context is "I want her (to come) home", but the alternative interpretation "I want (to own) her home" is linguistically equally valid.

[EDIT:] Oh, and in case it was the last bit you didn't get: Dad's telling the daughter he loves such a wonderful candidate for son-in-law, equipped as he already is at a tender age with such a marvellous sense of dad humour. [/EDIT]