For me, if you were to add "คนเดียว" to the end of the sentence, it would equate more to this:
- My father loves only my mother
I.e. It would mean that the father loves the mother and nobody else.
So I feel the original translation is more accurate, as it doesn't limit the father's love in this way. For example, it could be extended in this fashion:
- My father loves my mother, and he loves me too.