
Uday M. answered 07/30/19
M.S. Engineering, 5+ years of teaching experience
Generally, "unbearable" is indeed used in negative contexts. You hit on it with your point about "to bear", because if you can't bear something (you can't manage it), it's probably going to be a bad thing. If you look at synonyms, you'll find words like insufferable and intolerable, which clearly have negative implications. If you're looking to convey the scale of something like curiosity, you can use words that more directly mean that, such as "considerable". For example, "As a child he had a considerable amount of curiosity..."
The way you've currently written the sentence would indeed imply that the mother was frustrated with the child's curiosity.