We discovered that our district allowed dual-enrollment which meant that we could teach academics at home during part of the day and still allow them to attend public school for part of the day for the special activities.
I first contacted the Home-School Office for our school district and she helped me through the process of dual-enrollment. After appropriate paperwork was filed, I coordinated with the principal and our teacher to decide on a schedule that worked for the school and for our family. It was amazingly simple to set up!
Our family has loved the balance this has brought to our home. We are able to rest assured that she is getting a good academic education and she is still able to have a social outlet.