Her children were born here, they could sponsor her if they are 21+ but the problem is her arrest in 2013 for using a fake/stolen social security number at a job plus being deported this week. Form I-130 is used to sponsor a parent for a permanent residency, and while it does not have anything about arrests it does ask if the person has had previous immigration issues and deportation would count. I sponsored my wife's parents as PR's and it took about 3 months to process in 2012 after which they can come and go without problems (they are chinese).
I'm not sure why they didn't try to legally bring her into the country before this, I believe her husband and both kids are citizens so while there may have been a period during which she had to reside outside the country while a I-130 is being processed, as it stands because she was actually deported things become much, much harder. I-130 does not bar people who are deported from being PR's, but it essentially becomes up to a judge to push it through since I'd imagine the default case is denial.
