Remember, water flows through the path of least resistance. While the pump may end up being sized large enough to push water through the secondary system, it will not do this unless doing so would require less head to accomplish.
If you have a loop 6" by 100' long (15 ft head), with a secondary loop off of this one at 4" by 50' long (20 ft head), the pump will only pump water through the 6" pipe because it takes less energy to do so. An improperly sized pump will just follow the pump curve to the actual head loss of the system (higher flow than intended), look at a pump curve, you should be able to figure that one out. A problem occurs with this because now you may end up cavitating your pump (beyond the limits of the pump curves).
The only way to get the primary pump to pump through both primary and secondary systems is to add a block to the primary system after the secondary system branch off. The blockage (valve, coil, whatever) would need to have a head loss that equaled or exceeded 20 ft. head loss to make the pump want to divert down the secondary line.
Run some system head loss calcs using different paths. If you know what you're doing, you should be able to see how the pump will be effected.
PS. If the primary pump is oversized, crank down on the balancing valve.