It's easy to get caught up in what we believe we owe our parents. But we shouldn't forget what we owe ourselves, or our children. It's great that your child was able to communicate her discomfort to you. She has let you know that she 'really, really' doesn't want to visit your mom. And now I think she needs you to pay attention to those things.
As the father of kids who are right about those ages, I can concur that it's probably not a great idea for my kids to go down to the dock unsupervised even though they can swim and won't jump in or get pulled in by some giant man-eating horseshoe crab. If it were my kids, I would never leave them alone for more than five minutes.
I get it. However, she continues to be disrespectful to me and has made him choose sides in disagreements. I've always tried to be neutral in situations. We all live together, but Amber and I just don't get along. She doesn't respect her father at all. When I have tried to make him realize it or support him when she's being unruly, I am turned into the bad guy.
My close friends have several kids who are generally "OK" as kids. I've had some fun conversations with the kids as they've grown but my issue is one of the kids ("Alex") was babied (parents acknowledged this) and her behavior has really gotten out of hand. Think weaponized incompetence, neediness, unhelpful most of the time accompanied by extreme attitude and yelling at the parents when asked to do something she doesn't want to do, often relies on their other siblings to do things for them-and she's the oldest!