Normally it is up to the ME (Medical Examiner) to decide if an autopsy is to be done or not, otherwise the family can request one at their expense. In this case, the OP stated that they declined at their expense based on what they were told at the hospital. Usually, ME's decline doing autopsies on people with pre-existing medical conditions of high mortality and are elderly because they are swamped with so many cases of younger people killed due to crime; they don't have the manpower to take as many cases as they used to. Some states are worse than others, but it is a nationwide problem in the US. However if someone enters the hospital and dies within 24 hours, the case has to be run by the ME verbally/phone, and the ME can still decline (because of what I stated above).
I would also want to know the cause of death. Why didn't they perform an autopsy when the cause of death was really unknown?
Usually a clot to the lungs people are blue from the chest up, not a swollen belly. Did your father have something called an abdominal aortic aneurism (AAA)? It is something that is often undetected, and when the artery (aortic artery) bursts, it is sudden and causes immediate death and this can cause a swollen abdomen.
When a person stops breathing, they are not getting air, so this causes the face to turn blue no matter what the problem is.
If a person has any kind of surgery, one of the risks is what is called a "fat embolism" where a piece of fat from the surgical site migrates to the heart, lung, or brain and can cause sudden death.
Without an autopsy, there is no way of knowing for sure what happened. But it sounds like your father passed quickly so he most likely was not in pain or suffering.
I know this is difficult not knowing, and deaths that we are not prepared for are harder to deal with. If you are concerned, you have the right (or who ever his POA is) to request a copy of his medical records (the request will have to be in writing on their form). If you feel that there was any wrong-doing, an attorney can review the records, but most likely it was covered up or missed by the staff, and it is a long process which will only prolong your grieving.
Try to remember your father as he was and the happy memories you had with him as difficult as this time is for you. Yes, the story doesn't add up IMO, but it also sounds like he did not suffer either. I sense that you are concerned about him and you are a very good daughter. I lost my father 2 years ago and not a day goes by when I don't think about him and he also had a cardiac condition. Be proud of yourself and the relationship you had with your father. Perhaps you can do something to honor this special relationship you had to help you through this difficult time.