Oh, wow. My brain hurts reading that, and I can feel your anguish. It is sort of hard to offer advice without being right there to see the dog, but I have been in a similar predicament before. Twice, actually.
I'm not sure why your vet is acting like that, but whatever the reason, she doesn't sound like she's being very comforting to you right now. My gut sense would be to go to a different vet - one from a small practice who still gives individualized care. (I'm shocked that she sent you away that first day, and wouldn't be too happy about it!

What an awful experience! Perhaps she is rethinking what happened in 2011.)
Anyway, I think you need a fresh set of eyes to help you. I would ask friends today for a referral if they have a great hometown-type vet. I have had pretty good luck getting appointments talking on the phone to people and being succinct about what the problem is. Don't talk much about what happened in 2011 - you can figure it out later - as people might be afraid to take on your case if they feel that you are angry and accusatory. (Not saying you are; just saying avoid that discussion right now other than in a factual way, kwim? Sorry to be so direct.)
I remember the time I took this approach and the new vet took one look at my dog and said, "He's suffering". (We were prepared to put him to sleep but our vet wouldn't let us stay for the procedure

and so we had to find a new vet at the last moment. To complicate matters, we were also going away on a long planned vacation.) I said to the vet that I didn't want to put him to sleep just because we were going away, and he replied that that wasn't the case, we were putting him to sleep "because he needed us to to do that for him". That helped me keep it in perspective.
Now I am all for giving our pets as much time as they need if it works out for both the pet and the humans. But you are in a precarious situation here with whatever is going on with the rectal thing (is it a prolapse?) as it can't be comfortable and could subject the pet to bleeding, strangulation, infection or injury if it comes out in the middle of the night, say, etc. And then you have the issue of the vomiting, and I hate to say it, but the breathing heaviness usually means a pathologic process in the lungs. So you are most likely dealing with a metastatic, late case of advanced disease, and no, there is no cure for that, as much as we want to think there is for both people and pets. The most we can hope for is alleviation of symptoms.
I could probably write more, but I have to go now. The route I would take would be to find someone who can help you with hospice care, I'm pretty sure (not seeing the dog, but just going by my own experiences in medicine and what you've written here). Do find someone who's not going to rush you and your pet out the door in your time of need.
