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I'm making a minigame for my app and I just wanted to clear up some things before I begin...

I will have two rectangles, each will be on separate sides of the screen, left and right. I will have an image that spawns in at the top center of the screen and slowly falls down. I will use tilt controls in order to make the object in the center move left and right.

In order to register when the center image overlaps with a rectangle, how would I go about doing this? I would prefer if the entire image had to overlap with the rectangle before it was considered to have overlapped it.

>>> import ui
>>> a = ui.Rect(10, 10, 100, 100)
>>> b = ui.Rect(10, 10, 100, 100)
>>> c = ui.Rect(11, 10, 101, 100)
>>> a == b
True
>>> a == c
False

I think what you want is contains_rect, which you would apply to the bbox of the SpriteNodes.

IIRC you may be able to use in as well:
if other_rect in this_rect:

From the docs:

Rect.contains_point(p)
Return True if the given point lies within the bounds of the rectangle, False otherwise.

Rect.contains_rect(other_rect)
Return True if the given rectangle lies entirely within the bounds of this rectangle, False otherwise.

Rect.intersects(other_rect)
Return True if this rectangle intersects with the other rectangle, False otherwise.