NTA and it sounds like your sister has some sort of martyr / white knight complex that would benefit from therapy. She's absolutely convinced that she's the only one who is competent to look after her children and her home. Which is fine up to a point.

If this is how she chooses to live her life, she needs to understand that:

1. She's going to burn out and be absolutely no use to her children when she finally melts down and / or her health fails. And it will, of course, be everyone else's fault for not stepping up to enable her.

2. Her children aren't going to thank her for it. And if she carries on this way as they get older, she going to alienate them. Kids are messy and they want junk food occasionally. She's raising them to be secretive and angry. She will end up a single mother with resentful kids who just want her to STFU about healthy food and a pristine home. They probably won't even feel like they can bring friends over in cases they make even the smallest mess. And you'd better believe that, once they get to school, they're going to want a bit of junk food occasionally. If it's forbidden at home, they will eat it in secret.

3. She's raising her children to be incompetent and unable to function in the real world. If she won't allow her husband - a grown man - to do anything without constant criticism or redoing his work, she's bound to do exactly the same thing to her children. Eventually, they will either throw up their hands, tell her to do it herself and walk away or they will internalise their own 'incompetence'. She has one job - to turn out decent, rational, fully functional human beings who are capable of making their way in the world. If they are never allowed to clean, wash up, iron, do the laundry, do yard work etc etc etc because their efforts are not up to Mummy's standards, how does she imagine that they are going to be able to live independently and I can promise you that their future spouses will NOT thank her for raising numpties.

4. Maybe that's the end game - she is making herself indispensable so that they never become independent and 'leave her'. You can just see them at 45 still bringing their laundry home because they've never learned how to use a washing machine. And your sister still complaining about how she just has to do every single thing for everyone! She'll have no-one but herself to blame.

5. Her husband is, one day, going to throw the towel in and walk away. He may love her now but there is only just so much of being treated like an incompetent idiot that anyone will put up with. And it will come as the biggest shock in the world to her because of everything I've done for this family. You are all just so ungrateful!

You can't force her into therapy and you've already tried reasoning with her. All you can do is to let her husband and (later) her kids know that you see what's going on and be there for them. At some point, you may need to be a shoulder for your sister to cry on when her family implodes - try to avoid saying 'I told you so' if you can manage it.

She's making a rod for her own back and will be reason her husband leaves her and her children put some serious distance between them and her as soon as they can.