I don't know the relationships between Malone and Booth, yeah they might not like each other just like Luka and Nico did, but they have one goal, that is to make another run in the championship for this year and it seems that they are on track as they are still in the playoffs.
I searched on the net for the reason behind firing coach Malone and i see one of those is an internal conflict between Malone and GM Calvin Booth regarding roster construction as Malone wanted to field veteran players while Booth wanted to focus on young talents but sad to see both were leaving the Nuggets franchise.