The shortest way to get to Coorg from Mysore is via the National Highway 275. Mysore to Coorg distance by road takes around three hours and the roads are in excellent condition. First, you need to get to the Mysore Highway in Kajjihundi. Once there you need to continue on the Mangalore Mysore Highway till you reach Kodihalli K. G. This journey will take you about one and half hour. Then you need to continue along the Siddapura road till you reach Coorg.
The climatic conditions in Coorg are not that extreme so you can plan a trip here all year around, however, Coorg is known to receive heavy rainfall, so unless you're visiting specifically for the waterfalls, avoid visiting Coorg during the monsoons. If you’re planning to visit Coorg during the summer then always carry cool cotton light clothes so you can beat the heat. Hiring an air-conditioned cab will also work in your favor.
Apart from the route via National Highway 275, you can pick the Hassan Periyapatna road route. This route will take you about an hour more.
The roads between Mysore and Coorg are good but they can get congested due to the traffic. The road is smooth for most of the journey. You can definitely have a smooth trip with your family.