According to INS if she is illegal she will have to leave the country along with her kids. There is nothing you can do. Helping her stay after a divorce is illegal for you. She will have to submit proof of hardship and try to obtain a perm. residence on her own after the divorce. If you want to help her simply pay the filing costs.
Edit: Unless the kids are citizens.. be that I mean YOU are a natural born citizen and they were born here as well. If so she can easily stay here with her kids after SHE filed the petition on her OWN behalf. OR you both can file a petition now before a divorce and get her legalized based on the fact she has kids here... which could meet the test of hardship if she had to leave the country for proceedings. Really depends on how long she has been her illegally. If over a year illegal she faces a 10 year ban law which means she cannot reenter for 10 years. There is a waiver for this though, the hardship waiver.
yes she gets deported..
Yes.
Yes it would be the same as divorcing someone who abandoned you and you did not know their whereabouts.
http://www.vdare.com/mann/reporting_aliens.htm
Perhaps, but the mother should also be charged for harboring an illegal alien.
Unfortunately, an illegal alien can not become an US citizen if they have been deported before. If they have a felony, they can't become a US citizen either.
yup.
not the mother nor the baby
Can an illegal alien who was deported and barred for ten years come back sooner by marrying an us citizen?
The U.S. grants a married immigrant conditional permanent residence status for two years. At the time of the divorce if the two years has not past the spouse is deported after the divorce proceedings.
No it cant cuz it was born here
Of course! Being married does not affect one's legal status, even a legal alien can be deported for criminal activity.