The details of Israel's journey through and away from Seir are not clearly specified. There is vagueness in the words describing Israel's departure away from our brothers...away from the Arabah road from Elath and Ezion-geber.
The important point is that Israel is now advancing under the leadership of the Lord.
The second part of this verse marks the next stage in Israel's journey, namely, the approach to Moab.
8 So we went on, away from our brothers, the people of Esau, who live in Seir, away from the Arabah road from Elath and Ezion-geber.“And we turned and went in the direction of the wilderness of Moab.