While my own beliefs are more traditional, I can tell you about one of America's greatest thinkers--Ralph Waldo Emerson. He believed that God, man and nature are part of the same spirit. (He called it the Oversoul.)
You say that you are connected to people (your children) and to nature (your animals), so if Emerson, who was a very smart and spiritual man, was right in his belief of one spirit which expresses itself through God, man, and nature, then it follows that if you feel a deep connection to your children and to your animals, then you are through them also connected to your higher power.