Is there any way I can get my rebellious teen to want to spend more time with their family?

Every action has a equal and opposite reaction-Isaac Newton.  If you pressure them to do things they do not want to they will resist. The harder you push, the more resistance. Simply allow them to be part of the family dynamic at their own pace and time. They will come around to appreciate their family on their own. The only thing you can do is get out of the way so that you don't create more tension. 

Building relationships with your children begins at birth and is an on ongoing part of parenting. I work with teenagers and their biggest complaint is "My parents don't listen to me." Listen to your children and connect with them on their level. Do not become angry because they are choosing to isolate themselves. Try to relate to them and their world. Enter the world and mind of your teen. Communication and listening are the skills required here. I am not suggesting you befriend them. You are not your son or daughter's friend you are their parent.

Try to remember the feelings and emotions you experienced as a teenager. The hormonal influences and the changes your body experienced were profound, they will be the same for your teens too. 

Make the family environment a place where your teen wants to be and try and consider activities that will include all family members.