That's the worst part of the immigration thing. The kids don't have a choice in what their parents have done.
Personally, I think it's time to scrap the "if you're born here, you're a citizen" clause. Change it to read "You are only a citizen if your mother is a legal citizen at the time of birth". Consideration could be given if the expecting mother had applied for citizenship prior to becomming pregnant - if that is the case and she was granted citizenship post birth, then the child receives citizenship too.
In the mean time, I dunno. You could grant a visa until the kids graduate high school, then make the parents go back to Mexico unless they have applied for and received citizenship prior to HS graduation. But the loophole is, some would just keep having more kids to stay here.
I do think the citizenship/visa program needs to be updated and made more efficient. A neighbor (Mexican who legally became a US citizen) said it took her family over two years to be granted a two week travel visa to come visit her. That is ridiculous, especially considering they were following the rules!
We also have to find a way to secure the border - at least better than it is now. And severely punish employers caught using illegal labor. Real jail time for executives and maybe closure of business/forfeiture of assets would be a good start.
I'm not anti immigrant. I just want people to do it legally, and be proud of their new country/citizenship.