How do I sync an account that has Family Sharing access across multiple Windows laptops and Android phones?

I'm not sure I understand. Family Sharing is not supported on Windows or Android platforms. Perhaps you mean an Apple Family Music subscription. With an individual subscription to Apple Music you can use these devices:

Join Apple Music on your iPhone, iPad, iPod touch, Mac, or PC - Apple Support

Join Apple Music on Android - Apple Support

and I believe each individual in a Family Group with an Apple Music Family subscription should be able to do the same.