Can an illegal mother with USC child stays legally?

Can an illegal mother with two children(one is us citizen and the other is mexican citizen) stay legally in us? – Immigration – Avvo.com http://ping.fm/lZKaV

https://atomic-temporary-10880024.wpcomstaging.com/tag/family-petition/

https://atomic-temporary-10880024.wpcomstaging.com/tag/family-petitions/

https://atomic-temporary-10880024.wpcomstaging.com/tag/family-based-immigration/

https://californiaimmigration.us/waivers/237-waiver-in-immigration-court-for-family-entry-to-u-s-with-misrepresentation/