Arthur *was* a Clennam, Amy *was* a Dorrit?
As far as I can ascertain, on first viewing, Arthur was a Clennam, because he was the illegitimate child of Mr Clennam and a dancer, whom Mrs Clennam brought up as her own child.
Amy Dorrit wasn't related to any of the Clennams, but she was born in the Marshalsea on the day that Arthur's real mother died in poverty. Grandpa Clennam, having discovered all this, was outraged at the treatment of Arthur's real mum, and left a legacy to a child born in poverty in the Marshalsea. Amy Dorrit was that child.
Mrs Clennam saw to it that Amy didn't benefit from the legacy because that would have meant everyone knowing about her husband's (and by extension her) shame.
Have I got this right?