I would not put the shunt resistor in the ground path.
If the load ground were to get connected to the any other ground, then the shunt resistor gets bypassed, meaning the limit circuitry doesn't know what the load current is. Since the LTC7810 is a dual output product, the probability of the two loads sharing the same ground is high.
Putting the shunt resistor in the high side does complicate the current limit circuit a bit, but I think it's worth the extra effort.