OP, many people are extremely protective of their children, which in my opinion has the potential to make it harder for those children to develop skills of independent living (both practical and emotional) as they get older. Others allow their children more freedom and opportunities, which to my mind is healthier.
You know your daughter and know if she is likely to get upset being away from you, or likely to enjoy the opportunity to have fun with her friend and the excitement of a holiday.
If the latter, that's a credit to you and your partner, and the fact that you are raising a confident, secure little girl.
Don't let people on here make you doubt yourself. They just have a different approach. It doesn't make yours wrong.
I would definitely message and say to the mom that you need to know ASAP about the arrangements for dropping DD off on the trip. Say you are needing to make arrangements for that day for your other kids, so you just need to know timings. Obviously you can phrase it very politely - stress that you are grateful she is offering your DD this opportunity, etc etc. But something that conveys a sense of urgency.
She sounds like a nice woman, so I am sure she will respond as soon as she can, either by call or message, if you stress that you need to know. And it's only a couple of days away and she knows you have other kids and other commitments, so it's not unreasonable to say you need to know.
Good luck! I know what it's like - I can get myself into a pickle with things like this too, over thinking how the other person might react to what I say.
But you are being utterly reasonable in needing to know. And as long as you phrase it politely, it is always fine in my experience.