Go - How does one count territory in these two scenarios? (9x9)
You've misunderstood the scoring principle. White is, as you explained, diving the board. But that has no impact on scoring by itself. We often say, misleadingly, "divide the board in areas", but we should really say "stake out territory by surrounding it with walls". Only then can you count the score.

It is a bit tricky at first, but once you grasp it, it's very easy and natural.

$$W Scenario1
$$ --------------------
$$ | b b b X . . . . . |
$$ | b b b X . . . . . |
$$ | X X X X . . . . . |
$$ | . . . . O O O O O |
$$ | . . . . O . . . . |
$$ | . . . . O . . . . |
$$ | O O O O O . X X X |
$$ | . . . . . . X b b |
$$ | . . . . . . X b b |
$$ --------------------


In your first picture, player 2 has surrounded the corners (I've denoted that with 'b'). However, the other area is not yet finished, because it is not completely inside one player's walls. It is wrong to ask which side belongs to white, because nothing belongs to white yet - she did not surround any territory at all yet!

This means that this area is neutral and does not add score for any player. Instead, the players should continue playing and trying to stake out a wall around this area, naturally as large as possible. Let us try that.

$$W Possible result
$$ --------------------
$$ | b b b X b b X O w |
$$ | b b b X b X X O w |
$$ | X X X X X X O w w |
$$ | b b X . O O O O O |
$$ | X X O O O X X X O |
$$ | . O w w O X b X . |
$$ | O O O O O . X X X |
$$ | w w O X X X X b b |
$$ | w w O X b b X b b |
$$ --------------------


This could be a result. You can see that the previously neutral area has been divided, and both players got a certain share. You can see that now, white also has some area for herself (she had nothing before).

You'll also notice that after resolving, there are still some points on the board which are not controlled be either player. Because these points are too small to surround them, it is not needed to include them. Any player could play a stone there to remove them, but he would not gain any points, because he is not surrounding new territory. (I assume you're using Japanese rules, it's a bit different in Chinese rules.)

In your second picture black has 3 solid areas (2 of them are split into eyes). White, similarly as above, has no definite territory at all yet.