Anderson, of Clarell Walk in Thorpe Hesley, denied possessing an axe and knife.
The crash happened at about 03:15 BST on the southbound carriageway of the A1(M) between Chester-le-Street and Durham.
Appearing via video link from HMP Doncaster, Anderson spoke only to enter his pleas.
His barrister expressed “sympathy and condolences” to the family of those killed.
The family of Zackary and Ms Warner previously said they found “comfort” knowing they were “together”.
Zackary’s mum, Shalorna Warner, and his dad, Jack Blades, said their son brought “so much happiness” and they were “so sorry” he did not get to grow up.
The family said Ms Warner was “crazy, sassy, funny [and] beautiful”.
