This might be Marilyn Kaye's Replica series (I borrowed from my answer to Identifying a super-soldier novel with half-moon symbol).
"Replica" is a children's science fiction series about Amy Candler, a young teenager who discovers she is one of thirteen cloned girls who have been genetically modified to have superhuman abilities. She was created in the government-funded Project Crescent, and was kidnapped and adopted by one of the scientists after a change of heart. Throughout the series Amy struggles to live a normal life as the mysterious Organisation tries to use her and the other Project Crescent clones to create a master race and take over the world. Amy also seeks to help the other clones in the project, and encounters a number of other children and teenagers with genetic modifications or supernatural powers.
Amy is indeed a clone, the result of a super-soldier project. She essentially has peak human capabilities including extreme strength and speed, and the ability to pick up skills rapidly. In particular, Amy's abilities develop in the first book in her practice of gymnastics. As per your description, her mother rescued her when the facility burned out (implied to be sabotage whether by researchers, rivals, or Project Crescent itself) and Amy finds that there are more girls like her out there. Within the first two books, she meets one who is a French ballerina and one who is a minor movie star. She does have non-powered friends in her school.
It looks like books 6 and 12 deal with "Andy", who was genetically engineered to be her "perfect match", with more "Andies" showing up in the 18th book. That may be who you are remembering as her "brothers" since they were created in the lab in a similar manner at the same time.