Is caffeine-free, sugar-free soda okay for a 3-year-old?
While I wouldn't routinely give a child artificial sweeteners and caffeine, it seems to me that the amount he is giving her is unlikely to cause any lasting harm. On the other hand, at the risk of sounding like Dear Abby, are you sure that what he is feeding her is the real reason you are so upset?
Divorced parents tend to focus their anger on issues revolving around the children when they are really angry and upset with each other. Sometimes you have to put aside the smaller issues. In one of my divorced families, for example, the mother is vegetarian but the father is not. She accepts the fact that she cannot control everything in her children's lives, that they have the diet she prefers at home, and that they have a loving and involved father. The children understand that their mother eats a certain diet and father eats another. Conflict between the parents is minimized and the children are better for it.
Does your child's father take good care of her when she is with him? Is he loving and attentive? Does he keep her safeusing the right safety seat in the car, for example, and avoiding nuts, popcorn, and other foods she can choke on?
If he is a good father in all those other and really more important ways, I would relax about the small amount of soft drinks she is given.