First off, let me say it sounds like a really difficult situation, so my thoughts are with you. Can I clarify something, are the Military aware of your potential dx? It sounds like you're using a civvie Pdoc and therapist, is there not a military one you can use?
As someone who's ex forces themselves, I have to say that your health is of more importance than your service and whilst you're right that a dx may result in you being discharged, that would sadly be the right thing. BP is a son of a ***** and many of the behaviours it can cause are simply not compatible with working with firearms or in a military environment, though that's not to say there aren't roles you could work. You need to have a chat with your CO about the situation and how to handle your future. I'm sorry as this is probably not what you want to hear, but if you conceal it and are later found to have done so, you'll be in a world of ****.
I feel your pain about the family reaction, my father had BP and mine manifests itself very differently to him, so similar story to you. As you'll see, there's a lot of of advice and support on here, and many folk willing to chat things through and help guide you.
I wish you luck with it, as someone who has worked in several uniforms, and as someone who lost their job because of the BP.