And related to breaking the law and separation from your family, the kinds of crimes you need to commit for that to happen are usually much worse than immigration without a permit. Also, I wasn't thinking of the general idea of deporting someone who has children, but specifically to the cases of families who immigrated illegally, had a child in the US, and are now being deported while leaving a small child without care and with little hope of ever reconnecting with their parents. And the solution is not necessarily to let the parents stay, but to allow them to take their child with them.
Otherwise, your immigration policy sounds pretty nice. I am assuming you would also carve out exceptions for asylum seekers, but apart from that, it sounds positively utopian compared to anything like current practices, from what I've read.