Explaining boiling using internal energy
You are wrong when you say the potential energy of particles decrease when they move  apart.

The forces between the particles are attractive not repulsive.

Recall the definition of potential energy. It is the work done by external force on a charged particle under influence of electric field.

Therefore, the potential energy for particles, which attract each other, increases when they move apart.

So when to particles get close their potential energy decreases, hence their stability increases. This also happens to be one of the reasons why they come closer.