The following morning they did go to the beach, though not before spending a long time introducing Amy and Rory to Sophia and Jack. The group got along well, and soon Jack, Rory, Amy, and River were exchanging stories of their travels with the Doctor while they watched the children play.

Sophia kept mostly to herself. She clearly wanted to talk to the Doctor more, but she got the distinct impression that he was trying to avoid her. He was friendly to her, but any time she brought up Gallifrey he would shut down. She was far too great a reminder of everything he had lost. So after awhile she just let the matter rest.

When the time came for them to leave Hawaii, the Doctor asked Sophia and Jack to come with him, and they accepted. It wasn't much later that the Williams family was returned to their home in England.

One night not too much later when Jack and River were asleep, Sophia walked back to the control room where the Doctor was busy fiddling with various parts of the TARDIS. She watched him for awhile, wanting to talk to him but still not quite sure to approach him with some topics. He was friendly to her but she still felt like he was avoiding her most of the time.

"Grandfather, can we talk," she said softly as she approached his swing under the console.

He looked at her, his eyes slightly misty from her use of the family term, but he shrugged it off and smiled. "Of course, what about?"

"Gallifrey," she said simply.

He got up immediately and began playing with other parts of the TARDIS. "There's nothing to talk about. Gallifrey is gone. It was removed from time forever."

"Unless the time lock is broken," she said emphatically, moving herself in front of him again.

"That would bring about the destruction of the universe," he said quite gravely. "That's the whole reason the Time War was removed from time."

"But if the time lock were to be moved to the Void then it could in theory be separated from the terrors of the war."

He opened and closed his mouth a few times and then shook his head. "Only if there were a lot more Time Lords on our side to help control the variables and coefficients. Someone would also need to prevent Rassilon from continuing his madness."

"We already have someone in the council chambers. You saw her when the Master tried to overthrow the Earth, the man Wilfred Mott wrote about it. There was an older woman, she looked at you; she wanted you to know it was ok."

He looked pained at her words. "I can't depend upon her."

"Marek would be on your side no matter what, just because she refused to renew her vows to you doesn't mean that she stopped caring. She was working with Romana at the end, she helped me and the others escape."

He contemplated her words. "It still doesn't matter, there aren't enough Time Lords to do what you propose plus the timelock needs two keys to open and one of the keys is on Gallifrey."

"Which can be accessed at any time... Please, let us try."

Her pleas fell upon deaf ears. "Why do you refuse to let Gallifrey go?"

She realized that he was just as desperate to forget Gallifrey as she was to revive it. She laid a hand gently on his arm. "What about finding other survivors? Until finding me you didn't know there was anyone else. I have a list of names; we could try to find them."

He laid a hand on top of hers. "I can't, not right now."

She looked hurt and confused, but she followed his eyes to the hall and knew why. "River?"

He nodded. "She's pregnant, still only visible to people who know her well, anyone else would think she was just a little round in the middle. I can't endanger her or the baby."

She nodded sadly. "Then I guess we'll just travel together Grandfather."

River spoke up finally. She had been watching them for awhile. "No. Doctor, I know how much this means to you. We have time together still, time to raise our child. I can spend time with my parents while you three travel the universe looking for other Time Lords."

The Doctor took River's hands gently, he didn't know what to do or say. "I know that you'll return for me and our child. Go with Sophia, find your people. I'll be safe with my parents."

He gathered his wife into his arms and held her tightly. "Thank you," he whispered into her ear.

So it was decided, River would go to her parents for a time, and the Doctor would travel with Sophia and Jack while they searched for other Time Lords, wherever in time and space they could be.

Author's note: There's a specific reason why Sophia is convinced that Gallifrey will return.

In general I think that the woman in "The End of Time" is the Doctor's mother, but for emotional impact, his first wife works well too.