If the children are under the age of 18 and have no legal guardian, they can be deported with the parent.
She came here illegally, she committed other serious crimes while here, she was supposed to go back to her country or be deported. She is being deported, for all the choices SHE made. If she is separated from her family that is her/their choice. Her children can go back to Mexico or if they are citizens they can stay here. It is a choice they have to make, nothing on the rest of us.
She was here illegally, I have seen reports saying her husband is here illegally as well. If he is the father of the children then those children are citizens only due to this country being stupid enough to grant citizenship to babies whose parents have no legal ties to this country! I truly hope we change that policy as well.