Your daughter is right. Rats tend to keep mice away (or kill them). Muricide, they call it.
This is true it's very uncommon for rats and mice to occupy the same space, as for using a pet rat that's not used to finding it's own food I'm not so sure, might be a bit too domesticated.
@Dogs started
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Your daughter is right. Rats tend to keep mice away (or kill them). Muricide, they call it.