These are very tough cases under current immigration law. If your spouse enter the country illegally then she cannot obtain lawful permanent residence without leaving the U.S. This creates a problem because if she has remain in the country illegally for more than 6 months she will be barred from obtaining a visa for 3 years (10 years if she stayed illegally for more than 1 year.) In cases like these you have two options:
1. She can leave the country and you can apply for an immigrant visa and a waiver of the 3/10 year bar. The fact that she is married to a U.S. citizen and has a U.S. citizen child should weigh in her favor in the application for a waiver but there is no guarantee. Also, the process could take a year or more and this may not be a feasible option unless you are willing to relocate.
2. She can remain in the U.S. illegally, hope she doesn't get caught, and hope for a change in the immigration law.
I realize that neither are attractive options. There are many people in your situation and it is a difficult one.
If you decide to try to legalize her status now it is critical that you retain an attorney with extensive experience with 3/10 year bar waiver cases. Best of luck.
Your predicament is not as bleak as it may appaer. Waiver cases for spouses of US citizens are approved all the time, but they do take the expertise of a qualfied immigration practitioner who can map out a strategy, pre filing, that will aid in the approval of the waiver of the bar to inadmissibility. Advance planning pays off and only a creative and competent lawyer who thinks "outside the box" will be able to successfully assist you.
Her situation is a difficult one, but the way I see it:
1. She could wait for an amnesty if one ever happens. (Speculative)
2. She could ask for a waiver and apply outside the United States at the counsul in her home country.
Unfortunatly her situation is a difficult one. My question to her would be what country did she come from and what were the circumstances surrounding her leaving her home country?
These are difficult cases and very fact specific.
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