I personally feel a $100 increase is a lot at once. These families have not been with you since 2014.... so they may not understand you making up for 3-4 years without a raise all at once.
In your shoes I would increase my rates just above market for all new families enrolling and for current families increase rates 10% for your January 2018 timeline and then X% each year their after.
Build the annual rate increase of X% directly into your contract. Tom Copeland has a good article about annual increases:
http://tomcopelandblog.com/easiest-way-raise-rates
That said you need to do what you feel best with but in your shoes that is what I would do!