So, individuals seem to indicate that the Feat REALLY should be written as such:
Benefit(s): You still gain a buckler’s bonus to AC even if you use your shield hand for some other purpose.
Normal: When you wield a buckler, your shield hand is considered free for the purposes of casting spells, wielding weapons, and using any other abilities that require you to have a free hand or interact with your shield, such as the swashbuckler’s precise strike deed or the Weapon Finesse feat. However, you lose your bonus to AC when using your free hand for the aforementioned purposes.
Special: A monk with this feat is not considered to be using a shield for the purposes of his AC bonus, fast movement, or flurry of blows.
Yeah, it just doesn't make sense to include the example of using the Swashbuckler's Precise Strike Deed in the definition, granted that a Swashbuckler can already use Precise Strike, while wearing a buckler and fighting with a single weapon, and not lose the buckler's AC bonus.
So, the consensus seems to be that you may keep your AC while TWF. The questions that remain are (1) With this feat while TWF, can a Swashbuckler continue to use deeds such as Precise Strike? (2) Does this feat allow one hand to be considered free in that a Swashbuckler can TWF with Slashing Grace?
Long answer: Hand's Autonomy reduces the penalties for two-weapon fighting (the combat mode, not the feat). The various two-weapon fighting feats also reduce the penalties for two-weapon fighting (the combat mode). These reductions stack. The statement that the benefits "stack with the Two-Weapon Fighting feat" is technically redundant, as there's no mechanism by which they wouldn't stack by default. These aren't bonuses, just reductions of penalties.
But Hand's Autonomy's limiter is only on what Hand's Autonomy does, not what things other than Hand's Autonomy can do. So it's more than reasonable to interpret that the modifier granted by a thing you cannot turn off to apply before the modifier granted by the item you have to pick up or put on.
If it's Hand's Autonomy and another passive effect from a feat, those would not stack, but if it's Hand's Autonomy and an item, I believe they should.
I believe Melkiador is correct because both Dual-Balanced (DB) and Hand's Autonomy (HA) reduce penalties for Two-Weapon Fighting (TWF). HA will always reduce penalties by 2 to a minimum penalty of -1. If other feats or mods specifically reduce penalties for TWF as well, then HA will adjust to maintain that -1 minimum. In other words, with DB, TWF becomes -1 with light weapons and thus HA cannot reduce penalties any further. Even if you started with no weapons then added weapons, HA must maintain it's minimum -1 penalty, and as such it would adjust accordingly providing no benefit.
That being said, HA and DB would stack perfectly with one-handed weapons, which usually applying a -4 penalty that could be reduced to -1. It would certainly pair nicely with Weapon Focus as they target different aspects: penalty reduction vs increase to attack rolls.