Hi M.!
Potty training is so fun, isn't it?! :-)
Every child is different, so the only thing I can tell you is what worked with my daughter. Hopefully it will be helpful to you.
There were 2 things I did: one was advice my sister-in-law gave me. (This wasn't for pooping necessarily, but just toileting in general.) If she could tell her daughter needed to go, she would ask her if she wanted to. If her daughter said "no," she would very calmly say, "Ok, well mommy has to go potty. So I'll just go first." Then her daughter would run there and go, just so she could be "first" instead of mommy. This strategy also worked really well with my daughter.
The other thing I did that worked was to put a see-through container of Mini M&Ms in the bathroom on a high shelf. If she went poop, she would get 2. They're very tiny, so it isn't much of a sweet, and kids usually only poop once (or maybe twice) a day anyway, so it wasn't much. But my kids hardly ever get sweets so 2 Mini M&Ms was a pretty big deal. It worked like a charm.
Of course, I didn't start any of these strategies until I knew she was completely physically and emotionally ready and motivated. She had been asking to use the potty and trying it regularly. She was also able to stay dry for long periods of time.
Like someone mentioned earlier, part of the problem also might be that your stepson is at a different house half of the week, maybe with different rules. But your instinct is sooo right NOT to punish him for pooping, or leave him sitting in a poopy mess. It does make it much worse, and it can be hurtful to him.
Hopefully some of this is helpful. Best of luck to you!
J.