I'm thinking of making my ten-year-old daughter wear a bikini outside even when it's cold.
That's insane! Why would you make them wear that?
She can change when she's in the hot car
When its cold outside that isn't appropriate at all. You need to teach your kids what to wear and when to wear it.
I'm just trying to make her watch her weight.
Making her parade around in a bikini is not the way to do that. Fat shaming children can lead to mental health issues around their weight and even eating disorders. You should model good eating choices and cook healthy meals for your children if you want them to be healthy.