My former stepson had very big issues with potty training in general, especially pooping. It started when he was potty training and basically, I guess because of him having to be fully p/t for preschool, my ex-wife essentially had to "force" him into doing it right before he turned four. This was before I met her, but my understanding was that she used to have to have to watch him like a hawk, and drag him kicking and screaming into the bathroom until he got used to the idea.
The result was that when he was 5 and even 6, he still had a lot of potty issues. He was constantly "damp" -usually not to the point of soaking through to his pants, but his underwear were always pretty soggy. He wouldn't tell you when he had to go to the bathroom if we were out, and if you tried to take him, he'd refuse to go, to the point of having a screaming fit, then often wet his pants! After an embarrassing incident at Fantasmic during one visit to DHS (we were locals) we actually had him wear pullups the next visit to the MK (which proved to be a great idea when we got stuck in an attraction for over an hour!) Maybe not the most conventional thinking, but I'd take changing a few pullups and having an enjoyable visit over having bathroom battles on vacation, lol.
And he'd only poop about once a week, if we were lucky, no amount of fiber in his diet would change that, he simply held it in. Obviously, every time he went it would be an ordeal, but no amount of convincing that if he just went more often it wouldn't hurt didn't help. Not a road to go down if you can avoid it, for sure. I'm convinced that every child has a timetable, and while encouragement is one thing, too much pressure can have negative effects.
As for the pp who asked about nighttime, I know my former stepson's pediatrician told me that generally, night wetting isn't considered a concern in children until they are 7 or 8 years old, and there's nothing wrong with having them wear a diaper/pullup to avoid wet sheets and pajamas. Once a child goes 7-14 days dry, then you can have them try regular underwear. The children aren't being lazy (I know this isn't what the pp was suggesting), they simply can't help it, due to being deep sleepers, having undeveloped bladders, heredity (often the father was a bed-wetter, but if both parents were, your child has something like an over 40% chance of being one too!), or a combination of these things. You can't obviously train a child while they are asleep. No child enjoys waking up wet in the mornings.
One of the things they did suggest was NOT withholding fluids in the evenings/bedtime, which goes against conventional wisdom. But the idea behind it is that you want the child's bladder to get used to holding larger amounts of fluid so they learn to sleep through the night or wake up when they have to go. If you limit their fluid intake, you may actually be prolonging the amount of time it takes their bladder to learn. Made sense to me. He also suggested that a child can do "bladder strengthening" exercises during the day. All they have to do is when they feel the strong urge to go, try and hold it for a little bit. Start out small, maybe holding it for 2 minutes, then slowly increase the amount of time they hold it before having to go -5 minutes, then 10 minutes. This strengthens and stretches the bladder and can reduce and even eliminate bed-wetting in the long run.