The CHILDREN have right to be in the US; the PARENTS do not, having failed (in the case of malfeasant aliens, intentionally) to fulfill the legal paperworks to do so.
See the Canadian case of Joshua Key (his child is Can-Am dual, and thus--by your "logic"--has rights in Canada; BTW, they are similar to what I already referenced, and will refresh for you).
http://cnews.canoe.ca/CNEWS/World/2009/06/03/9663811-cp.htm lA US-born child can (upon reaching 21st birthday, if he/she so wishes) petition to sponsor parents as "immediate relatives"--the beneficiar(y/ies) will then be scrutinised by USCIS.
BTW, I have known more than a few families who have taken US-born children to India (which DOES NOT allow full-dual citizenship)--timeframe ranging from 1962 (when the option of OCI was not available at all; btw it still is not available for children whose parents are both Indian citizens) to current--to be raised there, undermining even the tenuous foundation for your argument!