In single player you can run a command that teleports a mob that is being ridden (In this case lets say a cow riding a pig) but on a server the command does not execute properly.

Commands
1) /summon armor_stand ~ ~1 ~ {Tags:["UA_Pack"],Small:1,Marker:1b,Invisible:1,DisabledSlots:2039583,Passengers:[

{id:"chest_minecart",CustomName:"UserAnimated's Backpack",Tags:["UA_Pack2"]}

]}

2) /summon armor_stand ~-2 ~1 ~

{CustomName:"UA_Teleport",CustomNameVisible:1,Tags:["UA_TP"]}

3) /testfor @p {Inventory:[{Slot:-106b,tag:{display:

{Name:"UserAnimated's Backpack"}

}}]}

4) /tp @e[tag=UA_Pack] @p

5) /tp @e[tag=UA_Pack] @e[tag=UA_TP]