Need to stay long term for kids medical treatment

U.S.C.I.S. will generally not allow an individual in your situation to remain here for a long time on humanitarian parole. If the agency decides to give you relief, it would probably place you on deferred departure under which you would not have a valid nonimmigrant status, but be allowed to stay with work privileges if you make such a request. Deferred departure would not allow you to adjust status in the US to permanent residence. However, if the agency allows you to stay for a long period of time, you may be able to qualify for cancellation of removal under which you would have to prove 10 years residence in the country, good moral character, and that your removal would cause exceptional and extremely unusual hardship to your US citizen daughter.Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

You will be able to extend your non-immigrant status for humanitarian reasons, but you won't be able to get a green card until your daughter is old enough to petition for you herself (age 21).