I have a nephew - my baby sister's son. My sister married a foreigner, one of the situations where he just wanted a green card. When he got what he wanted, and after beating her horribly, they divorced.
My sister became a single mom, with no education. She relied on my mom and dad to care for my nephew. At times, my sister was totally out of the picture for long lengths of time. My nephew loved my parents (his grands) and vice versa. AND he loved his mom - very much!!! The distances and the periods of separation didn't harm him. He had a stable home, a stable schedule, and caring substitute parents. My nephew (now in his twenties) and his mom are unbelievable close to this day.

This is food for thought. NOT a means of telling you what to do. I'm sure it could have gone the other way, given my parents fought, instead of accepted, the responsibility.

One more note: if Ana stayed with you, wouldn't it be just until the Olympics were over? Could periods of a week or two be carved out of DIL's training days? I hear Orchid so clearly about DIL using her window of health.
It saddens me that any of you have to make such choices over a sweet, literally helpless soul.
Can I have her? I have good references.