Well, despite still being unable to reveal about why kids conceived on the island could not survive, I guess there is a misunderstanding...

Spoiler Alert, click show to read: 
...about the Purgatory/Afterlife Warmup/Time-Free Zone/Whatever.

Flashsideways were the only part that Purgatory was depicted. Whatever happened on the island, back at home and back to the island again and in the parallel realities happened indeed.

What Flashsideways were the part right after Jack died/closed his eyes (noticed the worn tennis shoes -takes almost a quarter of the shot- as he stumbles back into the bamboos ?). It was the unified creation of the Losties where they could feel as best as they can. Jack had a son, Charlie could play on, Claire could have her baby, Locke could walk, Jin and Sun were free of their fears and together, Sawyer was not an outlaw -actually the opposite, Sayid could love what was lost to him and so on.

As senior Shephard said, "some before, some long after you" died. His implication of the non-Flashsideways experiences being real is further supported by Hurley claiming Ben to be the best #2 -remember him asking for Ben's help right after the moment "he was like John"-

Therefore I couldn't take your assumption about the children to be factful.