Translation:The family stops outside the restaurant.
I'm learning Norwegian myself, so take what I say with some caution, because it might be wrong: My dictionary (German-Norwegian) translates "å stanse" as "anhalten" which means "to stop sth from running". It even recommends "å stanse en maskin", so I suppose "å stanse" is used when stopping/turning off a machine of some kind. Maybe the family in this sentence is travelling by car. Note: The dictionary says that "å stanse" is also used when talking about stopping a bleeding.
On the other hand, "å slutte" is translated to "aufhören/beenden" which means "stopping with something you are doing".
Strandfloh's (see comment below/above) problems here are shared by me, a native British English speaker: I had been going to ask what this sentence supposedly means, but then read the comments and realized the issue; indeed, Strandfloh, an English person would not be likely to use this construction except in the case where one might stop the car momentarily outside a restaurant ( which in a town or city is unlikely to be possible owing to single or double yellow lines prohibiting "waiting or parking"!) for a few seconds. One might say,"Stop the car!" in an emergency. If one were waiting outside a restaurant to meet someone, for instance, the verb would always be that: waiting (or lingering....).