After this extract, do you continue to write with the point of view of Eri (or anyone in the car), or someone in the house, like the mother?
If you're writing from the POV of someone in the car, then don't use off. If you're writing from the POV of someone watching the car, or someone who ISN'T in the car, you can use 'off'.
Writing only 'drove to' seems to indicate that whoever is experiencing this actually saw them reach the main street. On the other hand, 'drove off to' indicates that the person saw the car driving away, he knows they're headed to the main street, but he doesn't necessarily know if they reached there or not.
Using simply 'drove off' can also be used if the destination is not given, or it isn't sure. For example, "I got into the car and drove off."