Question: My son is three years old and we have a great relationship. But his mother and I are divorced, and every time I go to pick him up he runs around and sort of avoids me. It seems more like a game than anything else. Once I chase him down and get him, we go off together, no tears, and everything is great. But when I drop him off, he runs away with no goodbye and it's disturbing. His mother is beginning to make noise that he doesn't want to be with me from this behavior. Other than this, everything is truly fine. Shouldn't she be helping the situation instead of doing nothing and complaining?
Answer: Taking you at your word that there is no further issue and that your son is not genuinely unhappy to see you or thrilled to leave you, it seems that you have something of a training issue. This is one of those divorce related issues that commonly gets out of hand quickly. If his parents were married, his parents would demand he give each parent a kiss hello or goodbye as a greeting. The obvious support of both parents creates a simple, easy resolution to training a child to properly greet others.
After divorce, there are these sad differences that cause further rifts between parents. Your ex probably feels that it's not her job to deal with this or worse, that she'd be covering up real issues that are occurring between you and your son. It would be ideal if she'd help and the two of you could stand firm together and teach this simple, well-mannered behavior. In fact, the behavior could be brought on by conversations she's having around your son in anticipation of your time together. In subtle ways she could be making your son anxious. Saying things like, "Everything will be okay with Daddy and I'll be right here when you get back waiting, don't worry," can send underlying negative messages that little kids feel and interpret without even realizing it.
However, there is nothing in the scenario you've described that would suggest that Mom is fueling this behavior. And many fathers have to reduce their dependance on mothers doing the job of parenting. It's not her job any more than yours to care for this situation and her distancing herself from it will help you learn to be a more complete parent and feel confident to manage these types of situations.
A simple solution would be to teach your child a secret handshake and greeting that you practice with him. The secret handshake can include a ritualistic kiss and hug as well. This way, through fun and love, you'll get your son in the habit of running to you to be involved in the "secret" greeting.