Turn out is essential for dancers especially ballet and contemporary genres. Turn out is asking the ball and socket joint of the hip to externally rotate to its maximum potential and then place movement and load into that scenario. Therefore the dancers not only need flexibility but also strength in this position.
Turn out muscles are and here is a picture of the anatomy. Some people have excellent flexibility of the hip but lack the strength to hold their turnout whilst dancing. Others need to work on the mobility of the hip joint through flexibility. It is good to balance the dancer workout with both strength and flexibility of the hip joint.
It is important that the lower back isn't over working in compensation of poor flexibility or strength in the turn out muscles. Other joints such as knee and ankle can also be compromised if the hip joint isn't providing the turnout and the dancer is trying to create a similar look through the incorrect avenues eg knees or ankles,
Here are some exercises to assist with turnout.
It is great to utilise a roller if you do not have access to one you can always do these exercises on the floor.
With the roller under the sacrum, which is the bony structure above the buttocks but be sure not to place it in the small of the back. Have the feet together in a small 1st position then float the leg into attitude devant then slide it under the supporting leg with turn out. Be sure to keep your pelvis balanced, settle the ribs so the back is not arching.
Place your legs in a figure 4 position and then
Draw the legs towards you and feel a stretch for the buttocks.
Sitting in froggy keep a long position of your spine as you hinge forward at the hips and bring your nose to your knees.
Lie on your front and whilst maintaining activity through the lower abdominals and keeping your pelvis neutral where you feel your pubic bone on the floor take your legs into a reverse froggy. It is important one does not arch their back. I do not suggest you do this in extension of the back it is about keeping the pelvis still whilst asking for turn out of your femur (thigh) bone in the hip.
Remember when developing yourself or other dancers it is not about experiencing pain. I do not believe in the saying no pain no gain. Smart training should allow you to achieve the best results without pain. Yes, you will feel discomfort but challenges and determination is part of reaching goals.