If you are in the US, the situation with therapy is similar to the child in college. Even though parents may be paying, the student's information about grades, and what they are doing remain confidential. There are ways for the child to consent to limited information- grades, financial information- to parents but parents dont get progress reports, or communication from professors. It's the same with therapists who are bound to HIPPA, confidentiality laws.
Still, there is a boundary and that is it's your money involved here and so you have the choice to pay or not- either for college or therapy or anything these. With therapy, its difficult to know what is actually going on. All you know from your D is what she tells you and all the therapist knows from your D is what she tells her. What your D tells the therapist has a big influence on how effective therapy is.
BPD can be challenging due to the pwBPD projecting, and perceiving situations from victim perspective. It's clear that you love your D and are doing all you can to be supportive of her and to help her make progress. It's discouraging when she blames others and you for issues that she is facing. This isn't about you as much as her perspective with her BPD. Her work with the therapist is entirely between the two of them. There isn't a way to have a specific timeline for progress, but even without that, there could be benefits to her from having someone objective to talk to, and be a source of support, even if your D isn't entirely transparent with the T.
Your boundaries are your money, your house, your rules- at any age. The employment situation is hard to gage but the cleanliness of the room, in your house, is. You can have expectations that your D maintains a level of cleanliness, while still allowing her the freedom to have her room as she likes it. It can be messy without being past a standard of clean. You can decide on what you can manage financially with regards to paying for therapy. These aren't easy boundaries, and expect your D to be angry and blaming for them, but without these, you and your H will feel resentful.
This is a difficult situation. It was the reverse for me in terms of relationships- my mother had BPD. Little was known at the time about BPD in her era and so the response of family members was to keep her from feeling stressed. However, without any expectations of her, she didn't accomplish things and so didn't become competent. Rather than to take on a task that she felt uncertain about, she would escalate her behaviors, blame others and so tasks were done for her in order to avoid her BPD behaviors but this perpetuated them.
She had therapy and while it didn't lead to a solution to her BPD, it may have helped in other ways, that we don't know about. It was strictly confidential to her. She was very sensitive to the possibility that someone would "talk about her" and expose her. We were not allowed any communication with her therapists and in addition, if she had a close friend, it was best for me (as an adult) to not have a relationship with that person and let that be her own world. As CC43 mentioned, your getting involved in your D's therapy can result in your D's losing trust in that relationship.



Tools and Skills