That was really a bad experience esp when travelling with family. I always fear this would happen someday since i do lot of weekend drive with 4 members + loads of items in trunk. First priority as you did is your family safety, which is way above money.
2nd think as bhvm said, get road side assistance by TATA, you will have details in the car Manual, on top, when you take insurance, like hdfc, they provide 1 year road assistance service. This does not mean it will be cheap, but will cost less than yours 6500.
Good luck mate with your service and hope TATA serves you well.
I don`t blame you but before going for long drive I take care of following things
1. Make sure I am fully equipped like torch, phone battery, car manual, insurance.. etec
2. Get basic knowledge on how to handle such accidents like ready manual or Googling
3. If you are using the same highway very often, save highway emergency phone number + list of TATA ASS
4. finally don`t panic. Safety is important and during cases like dog, save yourself because you dont know which vehicle is coming from behind, when you take sudden left. To avoid these animal instance, i always drive in the middle lane, this will give ample time to react