I think this is Mother to Elves by Michael Armstrong. The description matches, though it was published in The Magazine of Fantasy & Science Fiction, June 1994 not in Asimov's. According to ISFDB this is the only place it has been published.
The girl is Clara and she does have Williams' syndrome. The title refers to the elvish appearance that goes with the condition. Her mother is Beatrice.
The story starts at a doctor's surgery where Clara is diagnosed with the syndrome. Then Beatrice is visited by a team from the Navy:
So the naval officers explained it gently to her, one step at a time, so when Mrs. Thompson fully understood what they meant to do, she had to believe it. That Clara had Williams' Syndrome, that she was an elf . . . to the Navy, that meant one thing: she was special, and they wanted to take Clara away, away into space.
SPACE," SAID the tall woman, who told Mrs. Thompson her name was Anne, "space isn't quite what it seems. We think we understand it, but what we understand is like the soap that makes the bubble and we can't see through it to the air. You know what makes the bubble and you can see its shape, but suppose you didn't understand pressure, or air, or surface tension. You wouldn't understand the bubble, not really."
Mrs. Thompson nodded, politely, because she didn't see the point.
Anne sipped her tea and put it down. "It takes a special mind to understand space, to understand the inside of the bubble, the place we take our starships to get to other worlds. I understand that space a little bit, intellectually, I think, but I can't feel it. I could take you into that space but I couldn't get you out. To get out, we need someone who understands it, who feels it. So far, the only ones who can . . . are people like Clara."
People like Clara? It began to dawn on her, a bit. "She's special, I know that."
"You don't know how special. Do you know how many other elfin children there are on this planet, in all the known worlds, out. of all those innumerable billions of souls? None on Beyond, and of all humankind -barely fifty! Like so many genetic defects, we cured the pool of such problems. Only because not everyone has been completely screened has it been that the gene for Williams' Syndrome still exists. We'd change it back but first we have to find enough elfin children."
Normally the children are taken from their parents to be trained as pilots immediately after birth, but Clara was diagnosed late and the mother daughter bond has already formed. The Navy agreed to take Beatrice as crew so mother and daughter could stay together. The story ends:
Beatrice saw it then, saw her future and Clara's future. She would spend the rest of her life in space, on the school ship where they trained the navigators, the very ship the Mother Theresa now sped toward to deliver its two new crew.
Traveling in the same general subjective time as Clara would when she got her assignment, mother and daughter would grow old together, see each other often, and never be apart. Mother to Clara; mother to elves.
