D.B.
So both he and you think she's old enough to have a say, but he doesn't think she'll be old enough in 6 months or 2 years to have any more of a say if she changes her mind? Maybe he just wants things HIS way and not her way, and he's only giving in because right now "her way" fits in with his wishes?
He's in for a real shock in dealing with a tween and a teen. She's asserting her independence in this category, and she'll continue to assert in other categories. It's important to raise a strong child (particularly a girl, I think) who can resist peer pressure, choose wisely and really think things through. It sounds like you've done that because you say she is independent and resilient.
She needs a strong male role model, and if she sees her father through the week on a daily basis, she will see his good qualities and get a really up-close-and-personal view of his rigidity. If he doesn't get his way and goes crazy on her, it will be difficult but it will also be better that she sees this behavior and doesn't fall for it in another man later on. I think that's going to be the key to how you adjust and deal with things. If this works out, great. If it doesn't, she'll at least be doing it at age 12 and not running off with some dominant boyfriend who will break her heart and her spirit.
All you can do is be supportive of her abilities, let her know she's strong and resilient and can express her needs/wants, and help her brainstorm how she's going to get over the immediate hurdles of which clothes and accessories and school supplies and toiletries are at which house. This could make her stronger.
If you DON'T let her go, it will backfire on you and she will be resentful. If your ex is getting what he wants (or thinks he wants) and it doesn't go as smoothly as he expects, he'll have to adjust. He may wind up with a lot more respect for you (even if he doesn't admit it!) and realize that daily parenting is not easy. There will be different rules for your daughter, and she can learn how to adjust. This is what she wants and what her dad wants. So it's up to them to make it work.
My advice to you is not to pepper her with questions about her life over there, not to pass judgment on things that aren't done the way you would do them, and not to say "I told you so" when things get screwed up. Just keep supporting her in her abilities to manage, to negotiate her own space, and to communicate her needs. If he doesn't communicate with you and if he doesn't agree with you on anything, you let him handle things with his daughter.
Meantime, this is a way to start preparing yourself for longer absences, whether she goes to sleep away camp or eventually off to college.
But nothing is permanent! If this doesn't work out, it can be changed again. But everyone has to give it a good try! Meantime you will have some time with your baby and that can be a good thing!