I can't begin to understand what you are going through, but some of the feelings you have expressed I can recognise. I have learned a lot from some of the responses on here and I thank those contributors for their compassion and insight.
Trying to be a "present" (as opposed to an "absent") father is not always what it is cracked up to be. Having had a childhood where my own father made his priority earning enough money to keep the family together (often juggling three crap jobs a day) I did not manage to develop a loving relationship with him. I let that blight most of my life and could not stand to be near him. I determined that if I had children I would not let that happen to me.
When I became a father I stayed in a relationship that should never have happened for nearly thirty years, purely for the sake of keeping that promise I made to myself. Recently my youngest daughter, now twenty-five, informed me she cannot remember me ever being at home! Even the best intentions yield little reward at times. I don't know whether it is fair to conclude that we may have enjoyed a more productive relationship had I faced up to other challenges I was burying and put my own needs first. I'll never know, but it still hurts and feels like failure. Incidentally, your comments about public travel made me smile at the indelible memory I have of our Saturday trips into town, where she would scream, fight and cry without seeming to draw breath. Not only did I have to contend with the looks of other people who I knew were judging my failure to "control" my daughter, but on more than one occasion I had to account for the experience to the police who had been contacted by concerned onlookers. Sometimes the police traced me to home by being given my car number, the one that a little screaming, kicking, fighting toddler was being bundled into. Embarrassing, certainly, but I thank those people for being concerned and always asked the police to pass on my thanks.
When my marriage ended and I moved out I moved in with my by now widowed father ... temporarily. As events in his own life took a turn my temporary became eight years. While, to begin with, I wondered if we would last a week together let alone any longer we worked out ways of occupying the same space and over time found time and an ability to talk. It took me until I was in my fifties to build a relationship with my father. I grew to understand his motives for the way he acted, to know his deep regrets for his choices and came to love him. He died a year ago and I still think about him every day and I miss him so much it hurts. I consider myself very fortunate to have had a second opportunity to build a father-son relationship. Not many people have that chance. The point is though that, whatever life throws our way, it is probably not too late until it really is too late. Please don't give up hope.
I love some of the practical advice given already. In my life as a working musician I have had the privilege of working occasionally with people who live with conditions that make their lives (and the lives of people around them) very hard. I have worked with people who have been crippled and curled up in a wheelchair with cerebral palsy. One man I can think of had a little movement in one hand to operate the chair and a little movement in one foot. With the help of http://www.drakemusic.org he became a composer who composed music for films. Extraordinary things are achievable.
I don't know what the future holds for Edgar. I hope it is one that is filled with light and promise. I am in awe of teachers who work with children with severe disability and who learn to recognise tiny, almost invisible, steps as the milestones they are.
I can't think of a way that doesn't sound patronising to write this, but I wish you the strength and the courage to find your potential as a father and for Edgar to find and appreciate the love and support of a family who will come to know, understand and help him to realise his potential too. I don't believe any of this will be easy and it will be even harder without professional support, but there is support out there and a network of people who will want you, Edgar and his mother to succeed.