I think you have to let go. Your ex is raising 4 children, it was 8:30 at night on a school night, and he determined that there was no major problem.
The teacher apparently "yelled" at several children (if there was any yelling at all) so it wasn't all directed at your son. I disagree that anyone should have been involving the other child in the issue at all! You should not be telling your ex to interview or question another 6 year old in an issue that affects your son. She's 6, she lives in the same house, and she's not qualified to evaluate.
You do have to let your ex handle the bulk of the everyday activities. That's what you gave up when you let your kids live there. You have to find a way to trust him (which you did when you agreed to let the kids live there), and let them establish a daily routine. You should not be talking to the fiancee if you can avoid it - this is between you and your ex as parents of the 2 children you share.
Sometimes kids just don't report accurately what goes on in a classroom. I don't know if people have different expectations of male teachers - sometimes the deep voice alone is surprising to children accustomed to the all-female atmosphere of most elementary schools. Let it go. If there's a problem with your son, you'll find out about it at the parent-teacher conference (which you should attend with your ex, and his fiancee should attend the one for her daughter). If there's anything urgent, the teacher will contact you. If another issue comes up, you can contact the teacher via email but you have to stay calm and not explore every single thing that your son says or doesn't like.
I think you may be concerned about your children's new home and school situation, and you may be a little more vigilant about issues that most people get used to more easily when they are there and seeing the child's reaction overall. Sometimes kids on the phone over-emphasize things to a parent who wasn't there (same things happen when kids talk to non-custodial fathers or parents who travel on business). And it was 8:30 at night so the child had to have been exhausted, so maybe exaggerating. Sometimes kids don't like to be corrected by teachers - so they call it "yelling" when it just wasn't.
I think your ex and his fiancee might have gone overboard in saying that they had dishes and laundry, and you felt disrespected. But maybe they were frustrated because they have 4 kids between them who need to get to bed, and they themselves need to get up early to make lunches and get 4 kids ready for the day. They expected you to respect their answers, and you didn't.
Your problem is you don't trust your ex. That's something that needs work. Maybe he will step up to the plate more now that he has the kids so much. He can't be a horrible person or you would not have let the kids go there, right? So you made some decision that he's capable and that this can be a healthy situation for your 2 children. But both of you need to get used to this new arrangement. I'd leave his fiancee out of it entirely, frankly.
I think, as you get more used to first grade and the kids get more settled in with new teachers, these issues will work themselves out. Kids also have to learn to deal with teachers who discipline them, and even with teachers they might not like all that much. Looking back over my son's school years, I can see some great teachers and some how weren't so hot - but he survived and he learned how to work with difficult people. That's a valuable skill.
The best things you can do are to show your kids how to handle things calmly, talk them out, work as part of a group, and see that parents can split up and still work together to care for the kids they share. You need to have a good working relationship in case something urgent comes up.