Your clients need to speak to an immigration lawyer immediately. Illegal immigrants from Mexico are probably the topic of the most conversation and debate in immigration law today. The issues concerning Mexican people in Arizona (or I should say "Hispanic looking people" and the right to profile people to determine citizenship status) is one that has raised the level of awareness greatly concerning immigration issues, the difficult issues concerning profiling people based upon race as the discussion of proposed federal law concerning citizenship status for illegal immigrants who have been in this country for a period of time.
The children you describe are commonly (and somewhat crudely) referred to as "anchor babies" since there are allegations that illegal immigrants have children in this country so as to prevent deportation. I'm not going to discuss politics or personal thoughts but will just state that it does happen and it's unfortunate. Every case has its own specific details that could make a difference and, since this case has already involved the authorities concerning deportation, speaking to an immigration lawyer with all due haste certainly seems the most prudent action.