These are her most important years, her formative years, so the decision does matter.

If you feel you can give Anaiya a solid foundation, don't hesitate a minute to take it on. The rewards would be many.
What she is getting from her mom may be more of the weekend-X care, you know the parent who takes a child to Disneyland, doles out all the fun. In no way am I implying that your DIL does not love Anaiya in the fullest mommy capacity and is not treating her by way of that love. It's more to make a comparison between a disciplinarian and a fun-giver.

While focusing on the ball, Anaiya's mom may be juggling what comes first - child vs. Olympics. Pursuing the Olympics might bring big rewards which could be beneficial for the family in the long run. At the same time, it could break the family apart.

I can feel your frustration. If something like this were to happen in my family, I'd think of the grandchild before myself... and that would be so hard. I'd have to put myself in a position of being a parent again. I think I'd have the feeling of being used and feel I'd be repeating a job I'd already finished. That would be hard for me, really hard. When you love a little being so much, though, you have to put that consideration into place. It's not their fault things are as they are. They need an advocate for their wellbeing. You have wisdom that your DIL doesn't.

BTW, what does your son think of all this?

Dotsie has a good idea. Get all your thoughts on paper, give it a day, reread them, re-evaluate the situation, then have a family meeting.