I think if you were born here "You" have the right to stay here. Send there parents back, the ones who came here illegally and broke the law, with the option to take their kids with them or leave them here to prosper while they try to get in legally. I bet they take their kids with them. Breeding in our country does not guarantee you citizenship, especially if you committed a felony to do so.
And also to clarify my point. I am not advocating the state take their children from them. Just let them know that their children are natural citizens and they have that right if they want to leave them here, which will never happen. Problem solved.