I am really sorry to hear what you are all going through with poo problems. I can only begin to understand what you are going through. whilst I haven't had these experiences with DS or DD, I must have put my poor Mum through hell as a toddler.
I have very little memory of the whole time (other than a vague memory of the bottle of liquid paraffin under the kitchen sink), so what I can tell you comes from what I have learned from my Mum.
Apparently I potty trained very easily at 2 years exactly and was clean and dry day and night for a few months. The problem started after I suffered from post-viral constipation and passed a painful poo. This, combined with my ever-so-helpful sisters who would point at all productions in the potty and say something along the lines of "urgh that's disgusting", I decided I wasn't going to poo any more, ever.
I would hold poo in for about a week. At times I would be literally lying on the floor with stiff legs and screaming in pain, leaving me virtually passed out when the sensation passed. The compacted stools lead to 'leakage' which meant that my poor Mum was washing 10 terry nappies a day. In the end she was a virtual prisoner in the house as she couldn't take me anywhere.
This cycle lasted over a year, and the hv and GP were absolutely useless. The GP tried everything (in his opinion). He even, apparently, resorted to inserting a suppository in the middle of his waiting room (this was 1977 so you just didn't complain about your doctor's behaviour then). Eventually, my Mum saw a new GP, much more sympathetic, who said he just couldn't solve the problem and referred us to hospital.
The consultant there was, according to both my parents, marvellous. He said my bowel was completely full and severely backed-up, and that had to be dealt with first. He said that it would take time but eventually I would come out of it. I was prescribed liquid paraffin and sennacot .
Anyway, back in happies I was until everything had cleared out. After a long time and lots of perseverence the fear of pooing passed and I got into a routine. I was back in pants, but would ask for a nappy when I needed a poo.
This went on until one day I was in my ballet leotard and felt like I needed a poo. I didn't want to have a nappy on so my Mum suggested quietly that I go to the toilet and that was that.
To this day I couldn't possibly say why I did it. I have no major issues now. I survived two pregnancies - including two very difficult deliveries - without suffering from constipation. I am rather 'funny' about where I will poo. I couldn't possibly bring myself to do it in a public or shared toilet - camping is totally out for me! I'm also really paranoid about passing this anxiety on to my children (no signs of it yet), and get a bit anxious if they don't poo regularly. I guess I just have to get over it.
This all occurred in the 1970s so, as well as well as having no automatic wasing machine or disposable nappies, there was no Internet. Poor Mum knew absolutely no-one who had experienced anything like it, and had no-one to turn to for support. It wasn't until over a decade later when she was working as a health visitors' clerk, that she realised that other children did this too.
I am so glad my Mum was so patient and loving with me - there must have been times when she wanted to just walk away from the whole situation. I admire all your patience.