Author's Note: This story came about thanks to penguinspy42 and an observation that we've never seen the Doctor hug River on the series.
The Observations of Amelia Pond
"You know, I've never seen them hug?" Amy suddenly said over breakfast as Rory thumbed through the news on his smartphone.
"The Doctor and River." Amy waved her egg-ladened fork in the air before taking a bite. "He's hugged you and me quite a lot, but not our daughter? OK, it didn't count when they got married because you know, it was a wedding and all. But, just a proper hug."
"Really, if you look at the way River grew up, be surprised she hugs anyone. I don't remember her ever really hugging us when she was Mels," Rory pointed out.
"She hugs us now," Amy replied.
Rory coughed a bit. "They're married, Amy. I'm quite sure they at least hug upon occasion."
"I know. It's just one of those random things. Like when we were in Utah. He hugged us, but he didn't touch River."
"To be honest, he was in a giant robot."
"Which we didn't know at the time!" It was something Amy still needed to get the Doctor back for, letting them think he was dead. Oh, she knew he was maintaining the timeline and all, but it had hurt so badly at the time.
"I'm sure River knows how to hug a robot. She did snog one after all." Amy wrinkled her brow. "And, this has got to be among the oddest breakfast conversations we've ever had."
Rory stacked up his breakfast dishes and reached for Amy's. "Stop worrying, Amy," he said, kissing the top of her head as he took the dishes to the sink. "The River that visited us after Utah looked pretty content with her marriage. I'm sure everything is fine."
Three weeks later found Amy and Rory caught up in an adventure with the Doctor, where they had all wound up accused of being spies sent to introduce a dangerous bacteria to the local water supply. Actually, they'd been trying to eradicate the bacteria, but the king had turned the tables on them so he could use them as a scapegoat.
As they were forcibly escorted to the guillotine ("Oh, look, they've definitely made some improvements!" "Didn't need to know that, Doctor! Just for that, you die first!" "You're so Scottish, Pond!"), blasts of plasma fire rang through the room, neatly severing the king's head from his neck. A second shot, this one from a gun Amy didn't recognize, disintegrated the guillotine - blade and all.
As the guards fled, River strode into the room in an Elizabethian-style dress, curls piled high and a gun in each hand. Her eyes twinkled as she took in their disheveled appearances. "Hello, sweetie!"
"Oh, thank God, it's River," Amy said with a great deal of relief.
River kept the guns out until she reached the platform, then snagged the keys from the dead king's waist. "I expect the army will be coming in here after us in approximately five minutes, so we really should run," she suggested as she uncuffed Amy and Rory. She moved to the Doctor and gave him an appreciative look, eyes darkening. "Well, well, looks like someone already handcuffed you for me," she purred.
"I should have known you'd show up once they put them on," he replied.
"Oh, my love. Never could resist you being restrained."
"Right, that's a little too much information," Rory said, kneading his forehead.
"Hello? Impending army ready to kill us? Run now, flirt later?" Amy suggested.
River uncuffed the Doctor, and he made a sweeping motion toward the TARDIS. "Everybody run!"
They made it with seconds to spare, a spear lodging in the door just as the TARDIS disappeared into the vortex.
There wasn't a lot of small talk. They compared diaries, but it wasn't quite so dangerous now that they all knew not only who River was. Amy and Rory headed to shower and change. As Rory took his shower, Amy headed back to the console room feeling a bit famished. She wondered if she could get the Doctor and River to stop flirting long enough to consider tea. She had a craving for a pile of greasy chips.
She walked onto the landing and froze.
Below her stood the Doctor and River, their arms around each other. It looked to Amy that they'd been standing there for quite awhile, possibly since she and Rory had left. His head was bent to her shoulder, one hand buried in the curls that had been unpinned and now tumbled about River's shoulders. His other hand was at her waist, drawing what looked to be patterns in the small of her back. River had both her arms around his waist, under his jacket and looked to be smoothed over his back. They both looked so tired and weary that Amy's heart ached for them both.
Then the Doctor pulled back, murmured something, and pressed his forehead to River's. The look of absolute love and complete contentment they shared was so intense, that Amy found herself stumbling back into the corridor and into Rory. He placed a finger over his lips, took Amy's hand, and led her away.
They were back in their room before Amy could speak. "It's weird," she said. "I don't think I've ever seen anything that intimate in my life. Well, other than us, but …"
"I told you they'd be fine," Rory said with a small smile, rubbing Amy's back. "I saw them hugging like that a few weeks ago."
"And, you didn't say anything?"
"You said it yourself, Amy. It's pretty intimate. Even if I wanted to say something, it didn't seem right to do so. What they have works for them."
Amy grinned and hugged Rory. "Suppose so. Well, I was hungry, but I think I'll nap instead."
"I think I'll join you."