I think that other sports are very important and they are encouraged by all of our coaches. As a nation we have a problem of kids being less and less active each year and they cannot meet the recommended 2,5 hours of exercising by only doing gymnastics. Also gymnastics does not get them out of breath that often which is very highly recommended to happen several times a day.
We keep the hours on the lower side to make other sports possible. One day we had a little poll about activities with my 9-10 year old competitive gymnasts who do gymnastics 7,5 hours a week. ALL of them d other sports too and some of them also are in a sports program at school so they have PE class 2-3 times a week. They do soccer, dancing, figure ice skating, ballet, horseback riding and swimming on top of gym. Here are all the girls and their activities:
Girl A: gymnastics 4 times a week (includes one morning practice), swimming 3 times a week, school sports
Girl B: gymnastics 4 times a week (includes one morning practice), swimming 3 times a week, school sports, ballet 2 times a week
Girl C: gymnastics 3 times a week, soccer 2 times a week, dance once a week
Girl D: gymnastics 3 times a week, horseback riding once a week
Girl E: gymnastics 3 times a week, figure ice skating 3 times a week, ballet once a week
Girl F: gymnastics 3 times a week, dance once a week
Girl G: gymnastics 3 times a week, dance 2 times a week
Girl F: gymnastics 3 times a week, dance once a week
Girl G: gymnastics 3 times a week, soccer 4 times a week
Girl H: gymnastics 3 times a week, circus once a week
Girl I: gymnastics 3 times a week, soccer 2 times a week
Girl J: gymnastics 3 times a week, dance once a week
Most of them also walk or ride bike to get school and go to ski on weekends with their families but I still think that only half of them meet the required amount of activity a day. So if they tell me they have started a new sport I'm very happy. If they sometimes have to miss a practice to go to dance show or swimming comp I'm fine with that! We even sometimes have "LET'S TRY OTHER SPORTS TOGETHER!" days. We have went to circus class and swimming together as a group and also played outside and went to indoor activity park once. Next we are going to try baseball or volley ball. The kids love those days!
I would recommend you to take your daughter to the other gym. She's so young and she should't drop the other sports quite yet.