If you spawn a minecart riding a wolf using

/summon minecraft:wolf ~ ~1 ~ {Owner:"<Your name>",Passengers:[{id:"minecraft:minecart",Attributes:[{Name:generic.movementSpeed, Base:3.0f}]}]}

and push the wolf, it will start slowly moving in one direction, even sitting. You can stop it by placing blocks in it's path, and it follows you with the personal "Chest", but once it stops, it keeps on slowing "Scooting" one direction.

Also, if you modify the movementSpeed of the entity the minecart is riding, the minecart will control the movement of the entity until it runs into something, at which point the ridden entity's AI will take over. For example, run this command:

/summon minecraft:wolf ~ ~1 ~ {Passengers:[{id:"minecraft:minecart",Attributes:[{Name:generic.movementSpeed, Base:3.0f}]}]}

The wolf will slowly shuffle south until it hits a block, and then start running around at high speed.

However, if you isolate the minecart from the bottom entity by stacking another riding entity between them, the minecart will no longer affect the movement of the bottom entity:

/summon minecraft:wolf ~ ~1 ~ {Passengers:[{id:"chicken",Attributes:[{Name:generic.movementSpeed, Base:3.0f}],Passengers:[{id:"minecart"}]}]}