Can't teleport mounted mobs and the mob mounted on

I removed the tag from the first command as it is not formatted correctly and is not needed. Here is the command I used:

/summon wolf ~ ~1 ~ {CustomName:"test",CustomNameVisible:1,CollarColor:0,Sitting:0,Passengers:[{id:"wolf",CollarColor:0,Sitting:0}]}

Your command to teleport uses the tag target selector argument(tag=test), which is used with scoreboard tags. It is easier to use the name argument(name=test).

This would give you: /tp @e[name=test,c=1] @p

I ran this command and it does run properly. If you wanted to be more specific in selecting you could add type=wolf to the target selector.

This would give you: /tp @e[name=test,c=1,type=wolf] @p

This teleports them to the nearest player(@p). You can then be more specific with the target selector for the player to teleport them to.

Also, to note, if you were to name the passenger and teleport the passenger, it would split them up and only teleport the passenger.