"Without her it is not a family."
Translation:Bez ní to není rodina.
No, you cannot always translate it like that. 1. "Není" means "is not". 2. In many sentences you can leave out the personal pronoun. These are two separate facts.
Here you cannot leave out "to" because this is the very common sentence type "To je...", "To není...". You must have met it many times in this course.
Without "to" the meaning would be very different. "Bez ní není rodina." means "There is no family without her." I am trying to come up with a context where it would mean the sentence above, but all is really strange... like: (Tato skupina lidí) bez ní není není rodina. (This group of people) is not a family without her.