This story is not what it appears. The real issue is not the separation of children, but the detention of their parents. That's what the left really wants to stop. This action by Trump is intended to highlight that.
The Executive Order described in the article would permit children to be kept with their parents while their parents are being detained. But that's not what the left really wants.
What the article doesn't mention is that detaining children with their parents is against the terms of a Consent Order entered into by the Feds in 2015. In other words, the proposed Executive Order is unlawful. I suspect most ordinary people don't know that. This places the lefties in an awkward position, where they have one of two choices:
1) Allow this Executive Order to stand, thereby uniting parents with their children, but keeping the parents in detention, or;
2) Challenge the Executive Order as violating the Consent Order, thus preventing children from staying with their parents in detention
They don't really want the former, and are outraged about the latter. It's heads I win, tails you lose by the Administration.