I understand that ある means to live / to be. But I'm having trouble finding the purpose or translation of おしろに. I wonder if these two are working together to create some kind of meaning. It's from a children's book. The first line is むかし、(once upon a time), followed by the text above. My interpretation is that this means something to the effect of, "Once upon a time, there lived...". But I'm not understanding the specific action of the おしろに part of the sentence and so far haven't had luck with the dictionary. Any help is appreciated.
Before getting to おしろに, I'll talk about ある. The verb ある that you're thinking of means "to be / exist" but it's generally not used for living things. So it usually wouldn't mean "to live." Here it's not a verb, but a (probably etymologically related but different) ある that can only go before a noun and means "a certain ~"
As for おしろに, the core of it is しろ (castle).
In front of the core it has a kind of honorific / word-beautification marker お.
At the end is the location-marking particle に.
If we put everything together, あるおしろに means "in a certain castle."
Presumably the sentence continues with a description of someone living in the castle.