Here is long over due account of Wind's birth.
.
A week before Natasha's due date, she and Clint moved back into Stark Tower temporarily. Tony, and the Avengers really, had access to the best doctors and the tower was a safe place. It had been their home and they still considered the others family. This had been the plan all along and, besides, she had been coming to the tower for check ups and the ultrasounds, etc. There was never a chance that Natasha would set foot in a regular hospital or let strangers near her or her baby. That just wasn't going to happen.
There were no signs of labor for that entire week, and it wasn't until well into the next week that the time finally came. The doctors said, and Bruce had confirmed, that waiting was ok. Going a bit beyond her due date was no big deal and there was no need for Natasha to be induced. Besides, she was entirely against being administered drugs of any kind. And Clint had promised her that wouldn't happen. No matter what. During the waiting period, Natasha tried to keep herself occupied. Clint spent a lot of time on the firing range, sparring with Steve, or tormenting Tony. The evenings were regular Avengers down time; Poker, beer, conversations, group dinners. Tony seemed especially happy to have the master assassins back for a spell. Every time he saw Natasha he would nearly trip over himself to assist her with anything and everything. She found it funny, but also annoying. Any complaints she kept to herself though. Stark's generosity needed no thanks, she knew that by now. All he wanted was for it to be accepted, not rejected.
By that point, though, she was used to such behavior. Clint, now that he was among the others was definitely trying to play it cool. However, back at the house, or now whenever the two of them were alone together, he'd slip right back into over-solicitous-husband mode.
Natasha spent time walking the floors of the tower, chatting with Pepper, reading on the roof, and swimming. It felt good to float, especially with how unprecedentedly large she felt... and literally was.
On Thursday morning, roughly 5am, Natasha woke Clint from sleep. They spent the early morning hours playing cards in medical, just waiting, while the others paced around the tower and tried to distract themselves. None of them were above baby excitement. Steve practically turned into a grandma. At least, according to Tony he did. Jarvis was charged with immediately reporting the birth to all inhabitants of Stark Tower. Unbeknownst to Tony, Clint amended this command and told Jarvis not to call them until he or Natasha explicitly said to.
Close to 8 am, while Clint was downing his most recent cup of coffee, Nat's contractions began to come closer and closer together. After that, it was a pretty fast labor. By 9 am a screaming little Barton was being cleaned off while Clint held Natasha's hand, pushing her sweaty hair behind her ears, and telling her she'd done it.
The doctor announced that their baby was a boy.
"He's here, Tasha." He said so only she could hear.
"I hear him." She breathed, a big, tired smile stretching across her face.
Then she met Wind for the very first time.
It's silent in the room. Tony, Pepper, Steve, Bruce, Thor, the nurses and doctors, and all the rest have gone away. It's just Clint and Nat now. Clint, Nat, and Wind. A family. The lights of New York City twinkle and shine far below, expanding out for a great distance. Here, high above the madness is a peace that two people thought they never deserved.
Natasha has made space in the bed. Clint is sitting beside her now.
"He trusts me." Clint says quietly. The amazement in his voice can't be hidden. He's gazing down into his arms. His baby son is cradled there, against his chest. Wind is awake, wrapped in a blanket. Natasha has just fed him and now it's Dad's turn to hold him again. His little grayish blue eyes stare up at nothing in particular, but he seems to pick up on his dad's low voice.
"You're his father." Nat says, not to discourage Clint's wonder, just to taste the truth on her tongue one more time.
"I know, I just-" Clint doesn't need to finish the thought. She gets it. They both do.