Making three specific mobs ride each other in Minecraft?

Seeing your two attempts - You almost got it the second time around.

So, your attempt was:

/summon Pig ~ ~ ~ {Riding:{id:EnderDragon},Riding:{id:MinecartRideable},Saddle:1}`

Right now, your command looks like this:

Summon a Pig, riding on a Enderdragon AND a Minecart.

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To make your command correct, you have to nest the mobs correctly:

/summon Pig ~ ~ ~ {Riding:{id:EnderDragon,Riding:{id:MinecartRideable}},Saddle:1}

Which is:

Summon a Pig, riding a Enderdragon that is riding a Minecart.

If you want a mob that is riding another mob to ride said mob, you have to nest the riding tag inside the second mob.

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As stated by MrLemon in an comment, with the Riding tag being depreciated and being replaced by the Passenger tag (which is basically back-to-front) in the next version of Minecraft (currently active in snapshot 15w41a), we can use:

/summon MinecartRideable ~ ~ ~ {Passengers:[{id:EnderDragon,Passengers:[{id:Pig,Saddle:1}]}]}

Which is:

Summon a Minecart that has a Enderdragon in it which has a pig riding on it.

Or to simply put it: The above stuff but back-to-front.
Minecart-Enderdragon-Pig, not Pig-Enderdragon-Minecart.