What happened to Sophie and her family in "Hanna"

We don't know definitively.

We can certainly speculate though. A lot appears to depend on whether you want a happy ending or a sad ending.

Happy

In the original script for the film, Sophie (and therefore presumably the family) get quite a nice ending. Towards the end of the linked script is the following:

Sophie comes out in her school uniform. It’s a bright summer’s day. As she walks down the garden path, she reaches and meets the Postman.

SOPHIE Morning handsome.

He hands her a POSTCARD. Sophie opens the garden gate, reading the POSTCARD, there’s nothing on the back. On the front, PLANET EARTH. Sophie knows exactly who it’s from.

HANNA (V.O.) ...Earth is the only place in the universe where life is known to exist.

She walks down the street and the vast cityscape of LONDON spreads out in front of her.

Sad (and partially unconfirmed):

In the finished script for the film, these happy lines are removed from the ending:

HANNA steps out of the cabin. She's back wearing her furs again. In her hands she carries a cup of hot milk and a small wooden bowl. In VOICE-OVER we hear HANNA reading from her beloved Encyclopaedia.

HANNA (V.O.) The Earth is the third planet from the Sun, and the fifth-largest of the eight planets in the Solar System. HANNA sits down on a tree trunk outside the cabin and pours some milk into the bowl, then drinks a little for herself.

HANNA (V.O.) Home to millions of species, including humans, Earth is the only place in the universe where life is known to exist. She raises her head and makes a small clicking sound. Her friend, the snow fox, appears from the trees. The fox now has a small family of cubs. HANNA watches as the cubs approach the milk and begin to drink.

The highlighted section is what was said to Sophie on the postcard in the original script. As this scene has been removed, it certainly doesn't suggest anything good for poor Sophie and Miles.

As their fates are left unknown, I'd suggest it's nothing good and it's very likely they are dead.

TV Tropes does state: "A (German) poster later in the [film] says they are missing, so we can assume it was nothing good."

However, I haven't been able to confirm this (not least since I can't speak to German).