Bhagavad Gita promote harmony between our two selves the inner and outer. It is following the external self one indulges in religion, path of rituals. As a human being we have to take care of the needs of the family, the community and the entire world.
As an inner self we have a duty towards spirit, soul atman existing in our heart. Maintaining a delicate balance between two lives is difficult yet, not impossible. If we are in perfect harmony with our inner self then one becomes a Swami Vivekananda in real life.
As per Bhagavad Gita human beings always had two duties to perform, one for the inner self and the other for external manifest physical form. If as Siddhartha Gautama we decide to travel inner journey then we could not abandon our duty towards the whole family.
Karma simply cannot be burnt that way. We have to indulge in karma to demolish karma forever. Just by detaching self from karma we do not absolve self from karma forever. Just by touching feet of wife and child Siddhartha Gautama did not absolve self of karma. He should have taken permission of his wife and child before going to forests in search of cosmic truths of life.
For this grave mistake of his Siddhartha Gautama suffered all his life. So much so that he gained enlightenment only in the last stages of his life. Siddhartha Gautama became Gautama Buddha at the ripe age of 80 years; at 81 he left his mortal frame.
For a seeker of truth, one who desires indulging in life as stated in Bhagavad Gita the duty was indulging in nishkama karma yoga as detailed by Lord Krishna in Bhagavad Gita. Even a seeker has to indulge in karma but nishkama karma way of life, offering fruits of karma performed to God Almighty all the time. One has to work like a trustee, a caretaker like JRD Tata or King Janaka.
Without attaching self to fruits of karma performed is how a human being is supposed to live. Only that way could we fulfil our duty towards the family and also God. We can realize self, realize god only if we demolished karma in totality. Total demolition of karma can be realized only when we indulged in karma nishkama karma way of life.