I often say that it's ok for your children to see you upset, distressed and crying when going through divorce and separation.
It is important for them to know that you too are hurting because by knowing this and by showing your emotions, you are inadvertently giving them permission to feel the pain and hurt that the divorce process gives rise to and also just to show them that you are indeed human after all.
It's usually very difficult for a child, especially a sensitive one, to watch his mother cry or father fall apart and not do anything about it or feel that they are somehow responsible for the sadness or breakdown. They will very often do their best to rectify the situation by taking care of you, in the best way that they know; asking you if you're all right, if they can get you something or do something to make you feel better.
This is a very normal reaction to a specific situation but allowing to become the norm or go on for too long and you're changing your child's life trajectory. When a child become a caregiver they become your advisor, your mentor, the person looking after you. This set-up is definitely not conducive to helping children cope with divorce.
When a parent makes a statement like, "Sophia takes care of me. She doesn't like to see me sad and will sometimes just come and put her arms around to make me feel better," the first question that comes to my mind is, "And whom does Sophia turn to? What does Tom do with his own feelings and thoughts of fear, confusion and loss?
The answer to this is most likely she suppresses them or blocks them because there is nowhere else to take them. There is no adult container for their adverse and undesirable thoughts and feelings. There is no outlet, no vent so how are they coping with divorce.
"When a child turned caregiver tries to attend to her own needs and wishes, she feels guilty and undeserving...When a child forfeits her childhood and adolescence to take on responsibilities for a parent, her capacity to enjoy her life as a young person, develop close friendships and cultivate shared interests is sacrificed...it is an overburdening that seriously inhibits the child's freedom to separate normally and to lead a healthy adolescence..."
So, it is okay for your child to see you cry, be distressed and upset because fact is that the divorce process is a difficult journey for all to be on.
It is beneficial and advantageous for them to know that you are hurting too but, hard as it maybe, we need to continue being the parents and the adults in the room, the container and processor of your child's feelings of anxiety, fear and confusion in seeing the family unit he once knew disintegrate into something unfamiliar and foreign.
 Wallerstein, J., Lewis, J., and Blakeslee, S.,(2002), 'The Unexpected Legacy of Divorce: A 25 Year Landmark Study.'