How to practice effectively the concept of “attached detachment” and “detached attachment” in worldly life?

Imagine yourself traveling to a temple in an auto rickshaw. The auto rickshaw is speeding, taking left and right turns, stops for signals and so on. But you are silently sitting inside the autorickshaw without doing anything. Now tell me something. Who, at the first place desired to go to the temple, was it you or the autorickshaw? The autorickshaw that has no desires does the entire job, and you, who actually desired to go, are sitting silently. This is what Lord Sri Krishna says in the Gita, ‘See the Akarma in Karma and Karma in Akarma’.
Whatever you do, do without desires. If not, do it thinking of it as your duty. If not, do it in order to please the God or Guru.

A man is very much attached to his family. His sense of caring for their well being always keeps him tensed and worried. Is there a way wherein he can be mentally relaxed and free of worries? How can he attach himself solely to God?

When you travel in the bus, you are merely sitting. The moving bus is not the least worried. Only the driver of the bus and you are worried. Is it not?
Try to constantly remember and internalize the fact that your body is merely an instrument and the operator is none other than Lord Krishna. He is driving it. Then why worry?
One feels safe if he is employed in a big company with a huge turnover. One feels safe if he was born in a wealthy family.
Likewise, one can be totally free and happy in this world, if he surrenders completely to Lord Krishna, for, He is the supreme.

I am in my seventies. I am able to develop some level of detachment to children, grandchildren, even wife and in general wealth and its ramifications. My wife on the contrary has her concentration only on wealth. Please show me the way.

While you have developed a level of detachment for your family and children, let it mature enough to extend to your wife’s perceptions also.

Krishna says “Do not have attachments as it leads to sadness.” If a person is spiritual before entering Grihastashrama, it cannot be said he will be same after getting a family. I have seen people whose needs and wants have increased after their marriage. Wouldn’t marriage for a bachelor who is a spiritual aspirant make him more materialistic as will have less time for God?

These are generic statements that have been stated as a general guideline. However, it varies from person to person.
Intense spiritual Sadhanas foregoing family and the society is applicable only for Vedantis.
Bhaktas and those who follow the Bhagavata Dharma have always been exception to this rule. They never shy away from the duties of the Grihastashrama, and the Lord keeps them close to His heart in which ever state they are. Great Mahans who were Bhaktas of the highest order, like Jayadeva, Purandaradasa, Thiyagaraja and all the Pandarpur Sadhus are standing examples of this fact.