This is a common question/discussion we have in our office. Both for injury purposes and performance.
According to one study, “intense training in a single sport to the exclusion of others should be delayed until late adolescence (age 16-19) to optimize success while minimizing risk for injury and psychological stress.”
Specialized training in young athletes has an increased risk of injury and burnout. A general consensus seems to be that young athletes (age 0-12) should participate in as many different activities as they would like to limit this increase. This diversification in sport has also shown to actually be beneficial overall when an athlete picks a specific sport.
Check out one study here that has a lot of great information for you parents: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658407/