Well, as written it does not include a Hands: 1+ weapon. Whether that's intentional remains an open question, as far as my limited googling could tell.
By a RAW reading, the answer to your initial question is
"yes, but this does not apply to Brutish Shove".
Yes in that if you wield any weapon in two hands, it qualifies for any ability requiring you to wield it in two hands.
But no, Brutish Shove is not such an ability. It requires a two-handed (melee) weapon instead.
An ability that requires a two-handed melee weapon doesn't work with a 1+ weapon such as the Bastard Sword, since there is no rules language saying something like "a weapon counts as a two-handed weapon when you hold it in two hands".
Also, the weapon trait "two-hand" states:
Two-Hand: This weapon can be wielded with two hands.
Note how this doesn't make the weapon two-handed. It only allows you to wield it with two hands.
This is important because there is language that works the
other way, however:
Hands said:
In addition, some abilities require you to wield a weapon in two hands. You meet this requirement while holding the weapon in two hands, even if it doesn’t require two hands or have the two-hand trait.
Note how this allows you to wield
even a Shortsword in two hands to qualify for abilities that tell you to use two hands.
But again, Brutish Shove isn't such an ability as written. It's requirement is "You are wielding a two-handed melee weapon," not "You are wielding a melee weapon in two hands." A text search of the rule-book reveals three feats written like this: Brutish Shove, Knockdown (the ignore Trip part), and Positioning Assault.
In contrast, Advantageous Assault, Furious Focus, and Brutal Finish, has the "wielding in two hands" style language. There any weapon works, as long as you wield it in two hands.
So its an even split 3 feats using each phrasing. This suggests the difference is intentional, but I haven't looked deeper.