Hi Alison I do not know anything near enough about your situation, and this is only my opinion on the scant information you have given, all children will lie to some degree to cover their own misdeeds and protect themselves, however it would appear that your little one greatly fears your disapproval and so maintains her lie, unwittingly at greater cost to herself and your perception of her .
Children embellish stories often as a result of not feeling very good about themselves, they do not feel special enough and think that by exaggerating and embellishing this makes them bigger and better in the eyes of others, low self esteem if you like.
Children also lie as a form of seeking attention.
As said i dont know enough, but i would consider if she feels lesser for any reason in your eyes than the other two children, or that they get more attention.
Kids often dont really care how they get the attention they crave from parents and will often resort to negative behaviour, to them attention is attention.
i would say ignore it, let her save face where possible, if she is feeling crappy about herself then reinforcing to her that you think she is a liar aint gonna help, unless it become a major problem, while you find out the possible reasons for it.
celebrate her within the family , e.g so and so did this so well today, or i was really proud when so and so did this tolday, kind of thing, and make sure all of the children are recognised equally for their own particular talents and successes. it easy to praise the well behaved maths genius child, sometimes you have to get a bit more creative with the quirky kids.
spend quality time with her on her own when possible too.
We do try to be equal in attending to the children as we can but they all accuse me of giving more attention to the others. Hat though has always been a bit of a loaner and somewhat introspective at times, from birth she never liked hugs, she has started kissing me goodnight recently but most of the time you feel it hard to give the affection you feel towards her as she finds it uncomfortable. I will try to find better ways of giving her the attention she feels she lacks, hopefully without repercussions from the other too.
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1988 Specialized Rockhopper Comp