Hey Sinead
Good to hear that you have a therapist.
Its definitely common that pwBPD have a hard time getting into therapy, so much so there's this article here:
Getting a "Borderline" into TherapyDoes anyone have any tips on how to live with someone that is so moody, self absorbed and couldn’t care less about my struggles.
There's a lot of little changes you can make, mostly focused on yourself and how you react to his "moods".
From
What does it take to be in a BPD relationshipPreserve Your Emotional Health: The intensity of emotional reactions, and the rage take a toll on even the strongest. Since you cannot escape the natural human impulses to "recoil when raged" upon or "be overly protective" when idealized, it really important to have other outlets / escapes to keep yourself grounded. It's important not to become isolated. It's important to have a significant emotional support system for yourself (e.g., close friends) that goes beyond the relationship.
You mentioned taking care of your elderly mother, is there other family members who could provide a bit of extra support that you could lean on? Also, what about his moods would you say is the most difficult that you'd want to address first?