Lalitha as you said she very well knows how he is treated at his own home and she is being selfish by thinking only about her family and Shaurya..
I think she has given enough hints that she is actually thinking about him to refusing the alliance as she knows if he marries her his detractors read Mami and co will have another stick to beat him with .. they will say middle class keeda showed his true colors etc ... you know the kind of taunts she gives
Now the point about why she ignored the puppy..
We know she is in actual great pain about saying no and breaking the alliance .. one of the human reactions is that wen we are trying to move away from something painful we try to do away with everything that reminds us of that time or relationship..
People burn photos , delete contact numbers , change cities ..
The puppy reminds her of the haPpiest day in her life .. it is a reminder of her engagement that she is trying to forget..
Of course she will try to ignore it .. it is not that the puppy does not tug at her heartstrings.. she is trying to be hard hearted because she genuinely wants the best for Shaurya