If you weild a shield without proficiency, you take the proper penalties regardless of how many hands you have. I don't know what you mean by "does not use it during the fight." If you mean the alchemist carries it, but does not wield it, then the shield does not grant any AC bonus. However, that does not mean you can have a shield in an arm and decide each turn whether it counts as being wielded or not.


The two-handed weapon counts as a two-handed weapon, even if wielded with a shield. So yes, you get the better PA returns, and 1.5 times strength to damage.