If a grihasta is really serious about realizing the Self, and goes through the spiritual process while sustaining the family, then, wouldn’t s/he lose the interest in everything else like family/work etc? How can one continue to lead a normal everyday life, while seeking out to destroy desires?

When we do something, we either do it with attachment or we do it out of duty consciousness.
In office, we carryout the work sincerely because we are bound by duty-consciousness. There is no question of attachment here.
When at home, in family life, we carry out our duties with attachment.
We don’t show as much attachment in our office work as we do in buying a new shirt for Diwali or a new toy for our child at home.
The commitment that is shown in your family life should be limited to that of rendering your familial duties. If you can carry out your affairs at home with the same duty consciousness and no attachment to the activities, then you will be able to progress in spiritual life, while still being in family life.