I know someone whose dog was diagnosed with a very serious and lethal illness and an issue that came up was managing stress from this. The dog is having good days and not so good days. How does the humans involved with this cope?
One way is practicing some of the tools from ACT (Acceptance and Commitment therapy) which is a form of CBT. One tool is practicing being present. Use some of your senses to really notice things like looking at 5 objects or listening to 5 sounds. This can be called Mindfulness. We could practice Acceptance which is the practice of learning how not to struggle with uncomfortable sensations like the sadness or anxiety that can come up in a situation like this. It is also important to realize that not all of our thoughts are helpful to pay attention to so learning how to not attach ourselves to our unhelpful thoughts is also important.
A second way of coping is to make sure you allow yourself some time for yourself. If you don’t you may burn yourself out more quickly and or become more resentment towards your pet.
Take care.