It's really impossible to know what the individual outcome of forcing the issue will be until you look back on the whole experience. Kids are such individuals, and parent/child dynamics are so individual, that it's simply hard to know.
I have watched a couple of generations of kids being potty trained, and in almost every case, it appears that allowing the child to lead the process is what's most effective and painless in the long run. It does take longer, especially for some children (most often boys). But even after parents begin to despair that it will ever happen, every child I've personally known or heard about has finally just decided to go for it, and at that point, the training can take as little as one day.
From you request, I'm pretty sure you think you've been patiently waiting for your son to show signs of readiness. And it's hard to know without having been there, but if he's becoming hysterical when the subject is raised, then, at least in his mind, too much parental force has already been applied, and he feels cornered and completely resistant. This could happen as a result of one unfortunate event, or as a result of you and his daddy persistently urging, suggesting, bribing, insisting, etc.
And do check 'readiness' lists – there is a possibility that some crititical point of physical or emotional readiness has not yet been achieved (some helpful checklists, tips and pointers: http://www.parentingscience.com/toilet-training-readiness.... One way or another, he knows it's a topic of intense interest, something you REALLY, REALLY want from him. and he has put on the full emergency brake.
My suggestion is that you tell him that you trust him to get there when he knows he's ready. You respect that he has his reasons for not wanting to use the potty right now. You want to give him whatever time he needs to figure this out for himself. You might even ask him to get you one of his crayons to write with, and make a list of ALL the reasons you and he can think of for not wanting to use the potty. If he's clever and verbal, he can probably generate some reasons of his own that might surprise you. And you can add to his list, too, to show your complete sincerity. Little kids are mightily impressed by being taken so seriously.
Then don't say another word about it. Be prepared to offer nothing but cheerful silence on your part. No comments about big-boy pants, how much easier a potty would be, no frowns or comments while you change him. Give him some time to process. When he's convinced, in a week or a couple of months, that you are really going to respect his schedule on this, he may simply stop resisting. I've seen it happen several times with kids by the age of 4 at the latest (and I think some kids really have an emotional block before then that they need time/maturity to overcome).
This may sound like he could stall endlessly, but he won't, unless there are issues in your family or medical issues for him individually that need professsional intervention. He may simply need the emotional space to make that choice for himself. And honestly, kids do want to train when they are ready, just as they want to crawl, walk, and talk when they are ready.
I can really understand how trying it is for you to have three in diapers at once. Consider how much more trying it will be if you are forcing an unwilling child several times every day, and are cleaning up endless accidents and doing extra loads of laundry on top of it. Kids can be forced to sit, but unless you are going to strap him in, he may simply withhold until he's free again.
When I was raised, it was traditional to have kids trained by 2. I don't really remember my training, and neither does my mother, according to her. But she was an extremely forceful and controlling woman, and has raised 4 daughters who have dealt with emotional problems our whole lives, with varying levels of success. Once of my sisters has been emotionally disabled and living on the taxpayer's dime for a couple of decaded now. Once has sought love and understanding in a popular but unsavory cult. The other two of us have been luckier, but still struggled. Is any of this due to potty-training trauma? None of us have the resources to find out, but in my own circle of adult 60-somethings, there are several who have undergone extensive counseling to find out why they have huge issues with authority figures, or lifelong depression or rage, and have traced at least some of their misery and confusion back to potty training. It's so common in my generation, it's nearly a joke.
It it true? On an individual level, who really knows? But there's a lot of research on child development in the past few decades, and many studies to the real value in giving children more control over their own choices and decisions. Children who get to participate and are not simply raised according to old patterns of control have fewer emotional issues, perform better in school, have healthier relationships in childhood and adulthood.
Check this out yourself in books like The Science of Parenting – based on studies by brain researchers measuring the effect of different parenting techniques.
Also the book Raising an Emotionally Intelligent Child by John Gottman, and the concept of Emotion Coaching, another term you can google for lots of useful information. (Here's one good link to get you started: http://www.education.com/reference/article/important-pare... .) These are not on specifics like potty training, but whole philosophies of parenting that study the differences between Authoritarian, Authoritative, and Permissive/Negligent parenting. (As you might guess, Authoritative parents raise the happiest and most successful families).