Your parents apparent rejection - it's not about you, it's about them protecting themselves from being challenged on t heir lifestyle. I saw this with my best friend's parents - her father had dementia progressing rapidly, plus hearing loss, plus breathing troubles. He was also a violent bully. Her mother had osteoporosis so badly that her spine was collapsing and she was in total agony. She was a heavy smoker (bad for husband's lungs) and also took to drinking, to ease the increasingly severe pain. He would insist she sit with him at the table and play Scrabble (his way of trying to hold on to the last shreds of brain function) and this would severely aggravate her pain. She was going blind and had little sense of smell.
The overall result - she would fall, either from being drunk or from tripping over things he had put there to surround himself with familiar things. Her doctor would prescribe strong painkillers which hubby would find and throw away, or shout at her for taking them. Hubby insisted on cooking (he was a chef in his day) but would leave hot plates on, saucepans boiling dry. They would reheat leftovers that were sometimes two weeks old, and then they would get food poisoning. Both were losing weight. Their daughter prepared meals for them and froze them in neat little containers. her parents threw them away because "We won't eat that poor quality shop-bought muck" - the containers looked too professional, they didn't believe her that it was home-cooked, they accused her of trying to poison them.
All of this was an elaborate charade to convince the world that they were perfectly fine, thank you. No home help permitted - "I'll not have strangers in my house!" and the old man to be placated at all costs, to avoid his nasty temper. When an aged care assessment team made an inspection, this couple had practised and coached each other to a sufficient semblance of acceptability. There was insufficient reason to hospitalise them against their wills.
The house smelled - rotten food and stale urine. The old woman needed a walking stick but her husband refused to let her use one - "She's not old! Nothing wrong with her! Go away and leave us alone!" Because when people "snooped around" there was always the fear that authorities would intervene and take them away from their home, each other, their freedom.
I suspect your parents are desperate that letting anyone get too close will take away their freedom.
My friend's parents stayed together, on their own. One day the old woman, clutching to the arm of her husband because not only was she too weak to walk unaided, she was also too blind, was desperate for a drink and there was no alcohol in the house. She persuaded her husband to take her to the pub across the street. In this case it was the deaf and demented leading the blind and blind drunk - they fell on the steps. He broke his hip. At last they had to be separated. My friend rushed from work to find her father abusive but disoriented and hr mother frantic and demanding they be released from hospital to go home - the old woman was trying to refuse treatment for them both because of the fear of being "found out" and permanently separated from the old man. This wasn't out of love, it was out of fear for his violent temper and what he would do if she didn't do her utmost. She still kept screaming, "I love him, I love him, we promised we'd die in one another's arms," even as she insisted nothing was wrong with him, she'd nurse him at home, he didn't need surgery, etc.
My friend had to authorise her father's surgery and at the same time have her mother committed to a locked psychiatric ward as an involuntary patient. Things were very nasty, but in the hospital a medical examination showed both parents suffering severe malnutrition.
The old man never recovered. The old woman didn't seem to remember he existed. They never returned to the house. It cost a lot of money to clean, most of the contents had to be thrown away.
The old woman was admitted to hostel care with supervision. They have to watch her like a hawk to stop her getting access to alcohol and to reduce her smoking. The old man was transferred to the nursing home attached to the hostel, but she had to almost be bullied into seeing him. She would sit blankly, as if she didn't know who he was. He didn't know her at all. He'd lost his last marbles with the fall.
He died a week after the transfer. They managed to get her to his room before he died. She still seemed indifferent.
I was at the funeral, knowing all this. It was unbelievable. She was playing the grieving widow to the hilt - "Do you know, I was with my darling husband when he died... I held him in my arms." She milked every greeting with every guest at the funeral (I can't call them mourners) and quite a few were taken in. her immediate family were not, but there was no point calling her on it. She was going to enjoy her day, in her own way, rewriting history.
It was at that point that I really felt for my friend - because finally I could really understand what a rotten childhood she and her sister must have had, with this price pair as parents.
What you have gone through is probably far worse - at least my friend and her sister didn't feel compelled to leave home early. But from what I saw of this couple, everything they did in their last twenty years was geared to protecting the fragile world they'd built around themselves, each protecting the other's vices and nastiness, pretending it was love even as they abused each other. They had a fiction to maintain against the whole world, even from their own children (who could see through it all).
An utter, hopeless mess.
I strongly recommend that if/when you write your letter, keep one copy at least and have a ceremonial bonfire with it. It will probably give you more satisfaction than posting it off into limbo.
Like my friend, you are a survivor. You are your own best parent. They were only the genetic donors.
Marg