When parents are so upset with one another that they cannot acknowledge their own feelings, they may yet still look upon their child, the product of their union and feel their great love for their child. Accompanying the feelings of love for their offspring they also see attributes that are reminiscent of their spouse in the child. Whatever it is they see, it becomes impossible to relate to their companion with the same disregard when the wellsprings of love for their common child, their shared creation are overflowing.
Each and every Jew is a child of Abba and Ema. We are a physical body fused with a holy soul. The body represents HaShem, Abba, it is formed of nothing more or less than HaShem's own Will but it seems to us meer physicality. Our soul represents the Shechinah, Ema, it is the revelation of HaShem's light which was previously hidden within physicality.
When we perform a mitzwah with our soul and body in complete and total unity, we reveal our divine heritage both our Abba and our Ema. The fact that we are completely one in our observance, both physical and spiritual, testifies to the reality of oneness and singular reality of HaShem's light revealed openly in the world. The union of Abba and Ema.
This is the meaning of the l'shem yichud, for the sake of the union, which we say before the performance of a mitzwah. We are aspiring to show our truest self, and in so doing reunite our estranged parents in this long galut.