Natural Armor Increase (Ex): As his skin thickens, a dragon disciple takes on more and more of his progenitor's physical aspect. At 1st, 4th, and 7th level, a dragon disciple gains an increase to the character's existing natural armor (if any), as indicated on Table: Dragon Disciple. These armor bonuses stack.

First, the appropriate rules:

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Ironhide feat: Benefit: You gain a +1 natural armor bonus due to your unusually tough hide

Sorcerer Draconic Bloodline: Dragon Resistances (Ex): At 3rd level, you gain resist 5 against your energy type and a +1 natural armor bonus. At 9th level, your energy resistance increases to 10 and natural armor bonus increases to +2. At 15th level, your natural armor bonus increases to +4.

Dragon Disciple: Natural Armor Increase: As his skin thickens, a dragon disciple takes on more and more of his progenitor's physical aspect. At 1st, 4th, and 7th level, a dragon disciple gains an increase to the character's existing natural armor (if any), as indicated on Table: Dragon Disciple. These armor bonuses stack.

Savage Barbarian Natural Toughness: At 7th level, the savage barbarian gains a +1 natural armor bonus to AC when wearing no armor (shields are allowed). This bonus increases by +1 for every three levels beyond 7th.

Improved Natural Armor feat: Benefit: The creature's natural armor bonus increases by +1.

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The Ironhide feat, the Draconic Bloodline, and Natural Toughness provide the same benefit: "you gain [...] a +1 natural armor bonus."

Ergo, they do not stack; if you're a Draconic bloodline sorceror, don't bother taking the Ironhide feat (unless you want it at level 1 and your DM will let you retrain out of it later). Similarly, be wary of taking the Savage Barbarian archetype, unless your Barbarian level will be much higher than your Sorcerer level. (+4 Nat Armor
= Sorc 15 or Savage Barb 18)

Dragon Disciple improves whatever existing natural armor bonus you have (or, by ruling, gives you one if you don't have it).

The Improved Natural Armor feat improves your existing natural armor bonus by +1, and works just like the Dragon Disciple ability. (Note that it's technically a monster feat, and your DM may not let you take it.)

So, you'd take the best of Ironhide / Draconic Bloodline / Natural Toughness, and then add the bonuses from Dragon Disciple and the Imp. Nat. Armor feat to that.

Creatures which have a natural armor bonus of +1 or more qualify to take Imp. Nat. Armor, so HA's objection doesn't apply.