We are supposed to love God with all our heart, then what about our partner?

When you love God with all your heart, you will automatically love all His parts and parcels, including your partner. When you see God as the center of existence, you are rightly situated. When you see your partner as the center of your existence, you are in illusion.

Krishna says:

The living entities in this conditioned world are My eternal fragmental parts. Due to conditioned life, they are struggling very hard with the six senses, which include the mind.

The living entity in the material world carries his different conceptions of life from one body to another, as the air carries aromas. Thus he takes one kind of body and again quits it to take another.

The living entity, thus taking another gross body, obtains a certain type of ear, eye, tongue, nose and sense of touch, which are grouped about the mind. He thus enjoys a particular set of sense objects.

The foolish cannot understand how a living entity can quit his body, nor can they understand what sort of body he enjoys under the spell of the modes of nature. But one whose eyes are trained in knowledge can see all this.

The endeavoring transcendentalists who are situated in self-realization can see all this clearly. But those whose minds are not developed and who are not situated in self-realization cannot see what is taking place, though they may try.

The splendor of the sun, which dissipates the darkness of this whole world, comes from Me. And the splendor of the moon and the splendor of fire are also from Me.

I enter into each planet, and by My energy they stay in orbit. I become the moon and thereby supply the juice of life to all vegetables.

I am the fire of digestion in the bodies of all living entities, and I join with the air of life, outgoing and incoming, to digest the four kinds of foodstuff.

I am seated in everyone’s heart, and from Me come remembrance, knowledge and forgetfulness. By all the Vedas, I am to be known. Indeed, I am the compiler of Vedanta, and I am the knower of the Vedas.

There are two classes of beings, the fallible and the infallible. In the material world every living entity is fallible, and in the spiritual world every living entity is called infallible.

Besides these two, there is the greatest living personality, the Supreme Soul, the imperishable Lord Himself, who has entered the three worlds and is maintaining them.

Because I am transcendental, beyond both the fallible and the infallible, and because I am the greatest, I am celebrated both in the world and in the Vedas as that Supreme Person.

Whoever knows Me as the Supreme Personality of Godhead, without doubting, is the knower of everything. He therefore engages himself in full devotional service to Me, O son of Bharata.

—Bhagavad-gita 15.7-19