Why do you think Kisa Gotami understood this only the second time? In what way did the Buddha change her understanding?
Kisa Gotami understood that death is common to all and that she was being selfish in her grief. She understood this only the second time because it was then that she found that there was not a single house where some beloved had not died.
First time round, she was only thinking about her grief and was therefore asking for a medicine that would cure her son. When she met the Buddha, he asked her to get a handful of mustard seeds from a house where no one had died. He did this purposely to make her realize that there was not a single house where no beloved had died, and that death is natural. When she went to all the houses the second time, she felt dejected that she could not gather the mustard seeds. Then, when she sat and thought about it, she realized that the fate of men is such that they live and die. Death is common to all. This was what the Buddha had intended her to understand.