Discussion and hints:
For this problem, make your system big. In your FBD include A, B, P and link AOB. With this choice, you can simplify your angular impulse-momentum analysis since you do not need to deal with the impact force between P and A since it will be internal to this system.
Step 1: FBDs
Draw an FBD of A, B, P and AOB together.
Step 2: Kinetics (angular impulse/momentum)
Consider the external forces acting on your system in your FBD. Which, if any, forces cause a moment about the fixed point O? Write down the angular momentum for each particle individually and add together to find the angular momentum for your system: HO = 2m rA/O x vA + m rB/O x vB + m rC/O x vC. Is this momentum conserved? Also, consider using the coefficient of restitution equation.
Step 3: Kinematics
Use the rigid body velocity equation to relate the velocities of A and B.
Step 4: Solve
Use your results from Steps 3 and 4 to solve for the angular speed of AOB.
Any questions?