If your private disability is paying, I think that is a good indicator for your SSD chances. Those private companies do not pay benefits lightly. They investigate the cases,and they pay out when they absolutely have to. They are profit-making enterprises, so every dollar they pay you is a dollar out of their pocket.
In the meantime, it is not unusual to have to appeal Social Security cases, even when the applicant is clearly disabled and the claim is ultimately going to be successful. An appeal is not the end of the world. When your SSD claim is finally approved, you will get a lump sum for retroactive benefits, going all the way back to the date of onset of disability.
The date of onset is the date that the Social Security Administration decides that your disability started, which may not be the same as it actually started. But I don't believe that the official date of onset can be any later than the date that you filed your SSD claim. I don't know for sure if the fact that you are receiving private benefits will affect SSD's assigned date of onset; you will have to ask them or your attorney about that.
So be patient, but be hopeful. It's not time to be terrified yet. Save that for later. Maybe you won't ever need to be terrified at all. Definitely not yet. You have an attorney for your appeals (if necessary to appeal), and that is also good. SSD law and regs are very complicated, so a knowledgable attorney can be very helpful to you.
I have experience as a mental health center case manager in helping people to apply for SSD. I also have been on SSD myself, in the past. Based on my experience, the biggest reason why people are disapproved when they really are disabled is because SSD Disability Determination did not get all their records, or the applicant did not completely fill out the application. You can help by making sure you give SSD the names and current addresses of ALL the doctors and hospitals from whom you have received treatment. SSD is not going to go to a lot of trouble to investigate your background or to find correct addresses if you give incorrect ones, or to track down care providers who have moved on to different locations. You have to make it easy for SSD, if you want a quick and favorable decision.
And that big blank page in the application, where is says for you to give them any other information that you feel is important? That is YOUR page to make your case. That's where you tell them your medical history as you experienced it, everything you have tried to do to get back to work, how your symptoms affect you, what medication side effects you have, and basicially everything that you think they need to understand in order to understand why you can no longer support yourself. The majority of people leave this page blank, but that is like leaving a gift unwrapped.
Good luck. I think Social Security Disability decisions usually come out like they are supposed to, as long as the applicant does his or her part.
I'm all for collecting SS or at least disability until we feel confident or at least mentally better about the whole deal of having a heart event and more so should we need multiple comebacks to the hospital. However, at what point do we cut people off? I guess that's a political argument that can be made at some other point and on another forum. In the mean time, what makes you think you need SS?