I confirmed with a surgical oncologist about an infected central line, and you are right. This is a "pre-terminal" event and she will not recover from this without removal of
the line. But commonly, cancer patients will see a short improvement in health that preceeds death; one chaplain I know says it's a boost of energy to complete the things you need to tie up before you leave.
In response to your concern about what to say when she is thrilled she can eat: Feed her when she's hungry and enjoy it. Consider using her extra energy and mental capacity to take care of last wishes (you can call them something else) -- having her concentrate on "to do's" could be rewarding and productive at the same time. Some ideas might be to organize pictures or old letters, or write new ones. Plan a small gathering to celebrate an event, or a little trip.
But let's get back to the subject of denial. After years of caregiving to your cousin, you have established communications patterns that have worked in the past but are breaking down with these unprecidented happenings. I applaud you for still searching for ways to help her. Because this is all new to the two of you, it may be time to try something new in dealing with her denial about dying.
The work of two geriatric and palliative care professionals can help: Dr. Elisabeth Kubler-Ross and Dr. Joanne Lynn. Kubler-Ross's famous work, "On Death and Dying," outlines the five stages that she's identified during multiple years of research, one of which is Denial. Take a look at this website to read about the stages: http://changingminds.org/disciplines/change_management/kubler_ross/kubler_ross.htm
This will help you to understand her grief, as well as your own anticipatory grief. You're not immune from feelings, even though you've had to set yours aside before.
Dr. Lynn's work "Handbook for Mortals" is a beautiful guide to helping others toward end of life. You will find phrasing in both books that you can apply to your own situation, including questions and answers. You can tailor their recommendations to your needs. Here's a link:
It certainly sounds like your cousin has a wonderful caregiver in you. One last word of advice: Do not worry if you are not "succeeding" in communicating with her; you have done your job well over these years and she will understand in her own way, in her own time.