It's a silly plan with no long-term prospects, plus it won't really solve anything fundamentally, but it's exactly the kind of plan a child would come up with. At the end of the day, I reckon the (fake) duchess wouldn't be able to stand living much longer bearing such a secret and lie. Her position is incredibly stressful. Not to mention, she doesn't even have any control over her mother's situation, so she needs to believe in the goodwill of the scumbag count's family. Psychologically, it might also be better for her to reveal the plot, not to be exposed by the desperate (and stupid) real Alessa. The duke is not an idiot and probably would be able to see what kind of woman the real Alessa is, but it would still hurt any developing trust between the (fake) duchess and the duke if someone else revealed it all to him.
this looks like a setup for a successful self-sabotage. she will mistreat Clarisse somehow, earning the ire of the duke.
Hard to say. The real Alessa is not too smart, but she is a schemer, nonetheless. It's possible she won't try to hurt Clarisse directly, but will rather try to convince/manipulate Clarisse to work for her. If she tells Clarisse that the fake duchess must be reunited with her sick mother, and the real Alessa taking over the role of the duchess is the only way, I could see it potentially working against Clarisse. Of course the real Alessa's plan is still utter nonsense, but Clarisse is probably too young to understand too much of what's really going on.