In the first space animate the camera through to the point where the handshake is the entire frame (or larger). Create a new comp for your second space. In the second space animate you camera in that comp. In a third comp bring the two comps in and use the end of the first comp as a matte for the second.
Make a comp for each space, animate a camera in that comp and combine them in a master comp. This will help to keep things clear and manageable.
I’m sure there is a way to do it all in one comp if you wanted to.
TonyTony