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It's not the right thing for your child - that should be the end of the story. She isn't a toy to be shared out, or a token to be handed over as proof of trust - she is a toddler with her own practical and emotional needs, and there's no reason why she should be dragged away from her parents to spend the day with three people she doesn't know.
Without making any accusations, I really don't get why they are insisting you and dh can't go along too. Surely a family day out for all of you would be more fun and easier in practical terms?