I don't think you should remove her-she's bound to resent it, however I think you should have thought about it before, and thought about what you would do.
Dd1 got a scholarship to a private school, and one of our reasons for turning it down was that we wouldn't be able to afford it for both our other dc even if they got a scholarship. (She went for it due to strange games our secondaries locally were playing, but they did sort themselves out so it was okay)
There were other issues with the school, but it would have also been good for dd1, and also dd2 if we could have afforded it.
However I also know that getting or not getting a scholarship is out of the control of your dc and you. I suspect the school may well be less inclined to offer a second one in the same family (I certainly know that can be the case) because they probably really expect the second child to come too, may well even ask the older one if they expect to.
Also as they're usually a limited number, there's also the aspect that it's not about getting 90% or whatever, it's being in the top 3 (or however many). So you happen to have 3 exceptional children in one year, and your very bright dc may be well down. Another year, there's no one above the ordinary (or they've already accepted other places) and you can find your dc top by miles.
So having the situation that they can only go if they get a scholarship, although you can say "one got it due to their hard work" isn't as fair as it sounds.
In your circumstance I might try asking for a meeting with the finance person. Ask if there's any other help you can access. When they say there isn't, you say something along the lines of "Really sorry, then we'll have to turn down the place. We did want him to come here, but we really can't get the finances to work." And give the letter refusing the place.
Then they know it is financial reasons you have refused, and if they have any leeway (which they may not) they do have the option of coming back to you and giving you another option. They may look on you as low priority as you have a dc already at the school so may well come anyway.