I'm thinking of buying her bikini a size too small so my stepdaughter would feel motivated.
That is terrible. Do you want to make her feel bad about her body?
I don't care how she feels about her body. I'm more concerned about her feeling motivated to lose some weight.
What you are doing is damaging to her body image. Young girls are already pressured by society to look a certain way. Don't help that along.
I think she's old enough to handle it.
No one should have to deal with being shamed for the size or shape of their body. Trying to manipulate her into losing weight is a bad idea. She could develop an eating disorder or worse if you do that.