Once they are in the garden, a hot pepper spray will tend to repel the mites, but not kill them. Predatory mites will kill them and are completely safe for your child. Even safer than your insecticidal soap solution.
I guess the real answer depends on how healthy your native beneficial predator community is already. Putting them outside with mites already on them
might cause disaster by spreading the mite problem, but if your native predator population is high, it
might just be food for the predator mites, who will thank you for the free bonus food supply.
The fact that you had mites last year, but they were not a big issue,
tends to make me believe you have a healthy population of beneficials outside. But impossible to know for sure across the internet.