I don't think there's anything fundamentally wrong in sending your children to different types of school if you think those are the best choices for them. I know a family where the very academic dd went to an independent school and more average ds went to the local comp - both were happy in those environments, and got an education which suited them well.
But if the choice is only because of the finances, I would try to avoid that situation. You could end up with a later child who could have got much more from the independent school, who resents not having those opportunities. And maybe also the older child wishing they were in a less pressured environment!