[RPG] Does the multiplier for wielding a weapon two-handed apply to the Dex mod if I have the Weapon Finesse feat

They are not mutually exclusive

And in fact there's even one weapon that's two-handed but finessable (the Spiked Chain). You can Power Attack with a finesse'd weapon as well, unless it's classified as a Light Weapon. Did the designers intend this? We'll never know, but the RAW is fairly clear on the matter.

There's no text in Weapon Finesse or the section on using a one-handed weapon in two hands that forbids it.

I’m not a huge fan of using the FAQ or developer posts on the forum as a rules-source; on numerous occasions the statements made have made little sense, contradicted the rules or previous statements, and so on. And ultimately, I don’t really care what Paizo thinks the correct answer is so much as I care what’s best for my game. For the purposes of improving my game, I also care about what the rules actually say, so I know when I have to let players know that things are working differently.

So, with that in mind, I’m going to just stick to the wording of Power Attack itself:

This bonus to damage is increased by half (+50%) if you are making an attack with a two-handed weapon, a one handed weapon using two hands, or a primary natural weapon that adds 1-1/2 times your Strength modifier on damage rolls.

Emphasis mine. A two-handed weapon, even wielded in one hand, gets this benefit from Power Attack. Maybe that’s a good ruling, may it’s not, but it’s what the rule says; if I wanted to change it, I’d explicitly note it as a houserule.

Now, when you wield a two-handed weapon in one hand, there are two possibilities. Either the rules say “you may wield a two-handed weapon using one hand“ or “you may wield a weapon that’s normally two-handed as a one-handed weapon.” In the first case, it is still a two-handed weapon: it gets the 50% extra damage from Power Attack. In the second case, it is now no longer treated as a two-handed weapon, and thus does not receive that bonus.

In my own game, I’d happily houserule that anything that lets you wield a two-handed weapon “ as a one-handed weapon” still lets you apply the damage bonus, and furthermore that this situation lets you use two-weapon fighting normally even though it might still be treated as a two-handed weapon, because these sorts of abilities are very minor, and are often outrageously overpriced. The classes that receive them, or care enough about them to take them as feats, are grossly underpowered. Since I find that such power disparities make my game less enjoyable for all involved, I’d change it in a heartbeat.