Jennifer Lopez’s anxious dad, David Lopez, called his daughter twice a day in the weeks leading up to her due date to find out about the twins, says a friend. But he was hardly the only one on high alert. The entire staff of North Shore University Hospital in Manhasset, N.Y., was in a tizzy even before the arrival of J.Lo, 38, and her security-conscious husband, Marc Anthony, insiders tell Life & Style.

The hospital reportedly stepped up its security drills, which involve locking down the hospital in case a baby is kidnapped or otherwise vanishes. “They practiced the alerts twice a week in early February,” says a staffer. “That definitely had to do with J.Lo.”

“Babies have been kidnapped before,” a friend notes. “Jennifer had obvious concerns about security.”

Meanwhile, on a flight from London to LA on Feb. 7, Angelina Jolie, who insiders say is more than three months pregnant with twins, “started to get swollen ankles and nosebleeds and started having leg cramps,” says an insider close to Brangelina. “She fainted into her seat.”

Angie had a rough early pregnancy with Shiloh, too, but this time her symptoms are far more worrisome. As Life & Style reported, Brad and Angelina moved a full-time live-in nurse (with her own medical quarters) into their LA home in late January.

All of this is taking its toll on Brad, 44, too. “He’s a wreck,” says the friend of the actor.

For more about J.Lo and Angelina’s baby drama, check out the new issue of Life & Style, on newsstands now!