I use buttercream under my fondant. Sometimes I put it in the fridge first, sometimes I don’t. I spray the crusted buttercream with water before covering with fondant to allow it to stick better. Maybe try rolling out your fondant with some shortening on your table/rolling pin? Shortening sometimes helps give your fondant more stretch and keeps it from getting sticky which can help avoid those cracks.
-- Nikki, So Cal, www.Facebook.com/nikkibelleperchecakes