Living with in laws is an islamic concept? Did Imam Ali live with his mother after marriage? If a couple separates from their parents after marriage, it is said they broke the family, and as if committed a sin by leaving parents on their own in old age. How does Islam view this?

Islamic Law does not require married couples to live with their parents. We don’t have such recommendations. These are cultural.

Yes, one should not hurt their parents. So one must do their best to convince their parents and reduce their disappointment.