The FAQ about the unchained rogue's ability says that you get the two handing dex to damage on weapons you can two hand that work under your finesse training so I assume this also works if you use power attack?
Finesse Training has no bearing on whether Power Attack provides the extra bonus to two-handed weapons. If you are wielding a weapon in two handed and using the Power Attack feat you gain the extra damage regardless if using Strength or Dexterity to attack. Hopefully that helps.