Kids can't be killed, you can adopt a max of two, and I don't think you can disown them. So I'm pretty sure the only way to get rid of them is to delete Hearthfire, load your game so the deletion registers on the file, then redownload it.
I've only adopted one kid so far (the homeless girl that Hearthfire places in Whiterun), but the only time she runs up to me was to give me something, and when I come back after leaving the city (I kept her in Solitude while I was building the house). After that, she went wandering around, including going out into the city.
Not sure if you're aware of this, but you need child's beds in your house to adopt. Hearthfire houses have reserved spots for the beds (in the same room as your own, if you build a bedroom wing), but with the pre-existing houses something gets replaced. Whiterun replaces the alchemy lab (so they sleep in what looks like a closet), Riften replaces the enchanters table (they're stuck in the basement). Solitude actually has a really good one. The shelves outside the door to your bedroom are removed, and a door is put in its place. The kids get their own bedroom next to yours, in a room that didn't exist before.
Not sure about Windhelm and Markarth. Didn't have houses in those cities. Windhelm is big enough that they probably get put in a corner on the first floor, take over the other bedroom on the second floor, or their beds replace some of the useless crap in the main bedroom (there's a lot of useless crap in there IMO). The size of the Markarth house tells me that something will get replaced (it's about the same size as the Whiterun and Riften houses). Probably the enchanter's or alchemy tables again.
There are 10 types of people in the world. Those that know binary, and those that don't. Gamertag: Talon Omega
Nah i dont think you can get rid of them, i beat them lol and they still come back..i have 2 daughters and want a boy...my daughter even fault a giant with her fist -__- nothing happens..i think the best way its to just start over or like someone said here delete hearthfire and re-download it?