The linked article does not support your assertion that "immigrants with children tend to be a net drain". it simply says that the majority of this population uses at least one welfare program. it highlights low levels of education as the main driver of this, with the benefits usually going to the american-born children.

I suspect programs like Head Start and the school reduced/free lunch program account for a significant portion of the reported welfare use. Do you think that a poor immigrant family with working parents that uses these programs is a "net drain" on society?