I too recommend you read what Reine wrote ....then read it again. I can't tell you what to do, but I'll tell you what I'd do faced with an ultimatum from someone I love and whose love I believe in. I would meet her terms immediately ...at least temporarily. I would want to offer that as a sign that she comes first, without question. That also might provide a bit of a pressure valve to deflate some of her tension. Then I would look for the very first opportunity to have the conversation Reine suggested.
I suppose it goes without saying that this will be difficult. That she has delivered an ultimatum tells me she has reached the end of her rope; she may already have made up her mind about your future together, but is forcing you to pull the trigger. I agree with everyone who has said that getting a counselor involved is probably a must.
Keep in mind that anger is a secondary emotion; it is usually powered by underlying fear.
Best of luck to you in all of this.