Hi PersisBarry, you're doing fine! Welcome to the group -- we all started as beginners here.
It's also okay that you aren't sure whether or not your partner has BPD. Many members here have a pwBPD (person with BPD) in their lives who doesn't have an official diagnosis, but has many challenging traits and behaviors. We sometimes say here that it isn't the label or diagnosis that's the problem, it's what the person does that is the real issue.
Am I reading right that he is not your sons' dad?
How old are the boys -- younger teens or older teens? And how are his interactions with them?
With this most recent state where he’s thinking I’m the one that needs to take responsibility because of our issues, it’s really hard. He blames me for everything. Everything. I’m exhausted and I love him and I don’t know what to do.
Blame is a common thread around here. It's really frustrating to be targeted as the sole source of everything that could ever be wrong.
There are things we can do to "turn down the heat" so we can see if the relationship is livable -- for some members, the answer is Yes, after making some changes personally, using new tools and skills, there is enough good in the relationship to keep it going.
The hard part is that it falls to the non-BPD partner to take the lead emotionally in the relationship. This can often feel one-sided and unfair, but if you can make peace with the role of "emotional leader", there can be hope for change.
Part of that might include getting some therapy for yourself -- not because "you're to blame", more because we do better at interacting with pwBPD when we have a strong support system and healthy feedback on our part in the relationship. Unfortunately, many pwBPD struggle to be supportive and empathetic, and with "all or nothing" thinking patterns, often can't give healthy feedback. Getting the support and feedback from a neutral third party, like a counselor or therapist, will be so helpful in whatever path you take. Do you have a counselor already?
Keep us in the loop on how things are going;
kells76