I'm not any more bothered by illegal immigrants being separated from their children than I am by any other criminal who is routinely separated from his or her children when detained or incarcerated. Nor should anybody else be bothered if they thought about this issue rationally.
Somehow, many if not most people have subconsciously assimilated the media narrative that illegal immigrants are somehow a special class of people who are entitled to more privileges and rights than any US citizen who breaks the law.
BINGO!! Well put. As you point out, simple logic says incarcerated criminals, male or female, are separated from their children all the time. Why are we according these particular criminals more rights than American criminals? It makes zero sense. None at all.