My DS11 is about to start his second year in DI. At his school you have to be in 4th grade or older to participate. It is about problem solving, communicating, brainstorming, and thinking on your feet. It is in a drama like setting, where the team is presented a problem or challenge and they demonstrate their solution in a skit. I think it builds great skills, such as team work and speaking in front of others, not to mention the other skills listed above. Each team of 5-8 kids decides which challenge they want to do, then on competition day they are given some variables to incorporate into their skit with only minutes prepartaion time and are also given a completely new instant challenge. My son loved it and his team is staying together for this year. The challenge they chose last year and this year is the one involving improv, meaning they have even more unknown variables added on competition day. Its hard to explain, so I hope I am making a little sense. Google Destination Imagination and you will find the website, and maybe even one for your home state.
I absolutely can not imagine why a mom would hate it, because parents are not involved at all! They have a coach that can provide guidance, but parental involvement is strictly forbidden. My son would have practice for 1 hour right after school one day per week, and right before the competion date, they increased that to 1 1/2 hours one day per week and they would also practice during lunch recess. They each needed to bring in some miscellaneous supplies, like aluminum foil, paper cups, box, string, etc. that they used to make all their own props. The regional competition was one Saturday in a nearby town. My son's group placed 3rd. First and second place teams moved on to state and then those winners moved on to nationals. So, there is a small possiblity of travel, but only if they advance.
Our school had a parents meeting for DI, so parents could ask questions. Maybe ask the teacher who is in charge of the program at your school if you have any questions. Your daughter may really enjoy it if she gives it a try.