Answer
Embedded in your very first sentence is an independent question -- how does one carve out even half an hour or an hour for the worship of God amid household responsibilities? Although you have not framed it as a formal question, it is an important question for every householder, because 99.99% of people live in the Grihastha Ashrama (householder stage) and remain surrounded by worldly duties. In the light of the Gita, the answer to this question is useful for everyone. Therefore, I shall address this first; the method of Manasa Puja (mental worship) will be discussed later.
The Path of Nivritti and the Path of Pravritti (The Path of Renunciation and the Path of Action)
Some people are, by birth, inclined toward sannyasa. They have no interest in marriage, family, or worldly life, and from the very beginning wish to devote themselves solely to the sadhana of God -- for example, Adi Shankaracharya, Maharshi Ramana, or Shukadeva Muni. For them, marriage is not appropriate; rather, sannyasa is the natural, spontaneous, and superior path. Conversely, if someone is a householder by temperament and takes sannyasa merely out of frustration, betrayal, or cremation-ground dispassion (smashani vairagya), the likelihood of their falling from the path increases.
The second type of sannyasis are those who, in their declining years, after having experienced all worldly enjoyments and having been freed from responsibilities, choose a life of full-time contemplation of God. Often their life partner has also passed on. In such a state they retire into solitude and become absorbed in devotion and meditation. However, I have seen great souls who did not leave home but clearly told their children and grandchildren that they would no longer participate in their minor affairs or celebrations and should not be involved in them. Through proper communication and conversation, when family members understand the life purpose of an elderly person, they begin to cooperate, provided they see that the person is truly serious about their purpose. When children did not cooperate, such persons went to a sacred place, became absorbed in the remembrance of God, and departed for Vaikuntha from there.
But one who has married and had children can generally be free from responsibilities only when the education and marriages of the children are all completed.
However, it is often observed that even then, people become engrossed in their grandchildren and waste the golden period of their life. There is no harm in speaking with grandchildren occasionally, but their mind remains "engrossed" in them. As a result, they are deprived of Moksha and once again fall into the cycle of birth and death.
You are a householder and are fulfilling family responsibilities. You are not elderly either. In your case, taking sannyasa is not a natural option. Therefore, two paths are suitable for you:
1. Setting aside dedicated time: Hold a meeting with your family and, with love, have a clear conversation that you need one or two hours each day completely without interruption. Explain that every person has the right to spend a little time peacefully for the great purposes of their life. After repeated communication, the family will surely give you a time when no one will disturb you or call you. It need not necessarily be in the early morning. Then you can sit undisturbed in a room and practice meditation and mental worship. Let them know that you may be contacted only in an emergency.
2. Nama Japa during the remaining time: During the remaining 22 hours of the day, you can chant the Lord's name mentally. Nothing can obstruct this. In the Gita, the Lord Himself has said: "Among yajnas, I am the Japa Yajna." Japa is a serious sadhana.
3. Offering all actions to God: Do not perform the duties of household life as compulsion or merely as worldly responsibility. Perform them as the Lord's command, offering them to God. See how ordinary food, when offered to God, becomes prasada; similarly, any action, when offered to God, becomes His prasada, His blessing. This is the clear instruction of the Gita -- perform action for the welfare of the world (loka-sangraha). Then that very work becomes the sadhana of God. These are the very means the Gita has prescribed for householders -- that Moksha can be attained even while fulfilling worldly responsibilities.
I shall discuss the method of Manasa Puja in the next article.