When there are two air-circulation pumps (one powerful than the other) connected in series (as shown in the figure), how would the bigger pump affect the smaller pump?
The bigger pump affects the smaller pump by changing the system when it is on.
In this case, the bigger pump will cause the pressure at the inlet to the smaller pump to drop. The pressure drop will be proportional to the inlet pipe run. This pressure drop would reduce flow through the small pump.
One could imagine a scenario where a large pump causes reverse flow through the small pump. If the inlet pipe were short and/or large, the effect would be minor. If the pipe is long and/or small, the smaller pump might not even work.
There is no "best" location for the small pump inlet. The system just needs to be designed properly. If the small pump is sized according to the expected inlet and outlet pressure you should be fine regardless of its position.