Should I take my daughter to her regular doctor or to the sports medicine clinic for her sprained ankle?

Ankle Sprain. A well trained foot and ankle specialist can assist you with this. This can be a podiatric physician or a foot and ankle orthopedist. Look for board certified status and the recommendation of a family member or friend or your pcp.
Sports med. Most ankle sprains do not require surgery therefore so not require the care of the orthopedic surgeon. Sports medicine specialists with a background in pmr (physiatry), pediatrics, family or emergency medicine would all be good options and offer comprehensive non operative care.
Active? Depends on if your daughter is an active athlete. If her regular doc is familiar with her activities then stick with them. If she only sees her regular doc once a year and she is very active then a sports med doc would be handy for establishing a relationship and for any future injuries.
Depends. Oftentimes can start with the pcp for an ankle sprain, but certainly a sports medicine dr should be able to care for a sprained ankle (sports physiatrist, orthopaedist, primary care sports specialist). There are foot and ankle specialists as well.
Depends. If your pediatrician or family practice physician is interested/comfortable in treating musculoskeletal injuries then your regular doctor may be a perfect choice. The advantage of a sports physician is the skill in diagnosis, typically diagnostic tools and braces available if needed in clinic, incorporation of rehab program, clear plan for return to play. If your daughter is athlete- sports doc.
Specialist. Athletes almost always will recuperate much quicker with appropriate and aggressive therapy which is followed by initial immobilization. The specific timeframes are best known by specialists, and if there are any additional subtle injuries, a specialist will be best to identify these.
Depends. Many pediatricians are highly trained in evauating and caring for sports injuries. And generally they put your child's needs first, not the team or school. It is usually is more convenient and less expensive also. Often there is less unnecessary testing. And if they can not help, they will make the proper referral.
Sports Medicine Doc. Visiting a sports medicine orthopaedic surgeon will allow for the most progressive treatment to optimize recovery. Generally, a more aggressive approach is offered and a faster recovery is expected with a sports medicine doc.
Sports Clinic. I would suggest seeing a Sports Medicine doctor as he/she will be able to diagnosis and treat your daughters ankle injury in the most efficient manner. Best of luck.
Both can help. Primary care and pediatric doctors can certainly help with a sprained ankle. If she is walking on it 99% of the time it is not broken. If you are concerned however an orthopaedic md would always be able to help as well.