In a way, both can be justified. But I feel that Akshat was more right because of the following reasons: -
1. Amber's point is that they are not helpless even though they are conjoined. But suppose that Amber and Dhara were not conjoined. Then also it was important for them to inform somebody in the house (Biji or Akshat) that they were going out and when they expected to return. This is because they are staying Akshat's house.
2. Even though they are quite brave and consider themselves normal, it is a fact that they have faced problems. It is highly likely that they will face problems again. If it happens, then what will Akshat say to Lata? When Akshat has the responsibility, then he should have the right to know where they are going so that he can carry out his responsibilities properly.