How to develop compassion while avoiding attachment?

The Buddha stressed compassion in his teachings. It seems that the more one tries to be compassionate towards people, a natural tendency of attachment develops. For example, it seems that if I try to practice compassion towards my close family (and focus my mind on helping them), then I develop more attachment for them, and I feel closer to them and the pain of separation increases. Is it wrong that I want to feel closer to them? Did the Buddha have any advice about developing compassion while avoiding attachment (and other side effects like pride) ?