*Almost all child physical and sexual abuse takes place within the family/close friends of the family. Stranger abductions are vanishingly rare; abuse within the family is common.
Unfortunately, even people you know and trust may be a risk to your children. Also, unfortunately - as demonstrated on this thread - people massively overestimate their abilities to judge character and risk.
Statistically, a female neighbour babysitter is much, much safer than leaving your DC with any male relative or friend.*
I agree with this in terms of sexual abuse. But not-being-a-peadophile is a pretty low bar for selecting someone to look after your small children
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In all honesty this person would most likely be fine to look after them- although I would want to meet someone first , and know they had at least some experience with small children , before I allowed them to bathe my 3 year old and put them to bed!!
Even if she is the best babysitter in the world, she is a stranger to the children. That is an important factor too. How are they supposed to be comfortable settling to bed with a stranger?
Bed and bath time is not an appropriate introduction to an unknown babysitter.
If your DH wants to use her as a babysitter in the future , you should meet her first and then Introduce her to the kids for a couple of hours in the afternoon, or have her over to watch the kids after they have gone to bed. once both you and the children have some sort of a relationship/ knowledge of this person maybe she can do an evening bath and bedtime.