I certainly understand the point of view of the cleaner.
My mum had many cleaners, and she always tried to have them do "extra tasks". If they agreed one day, because they had some spare time, next time there would be other additional tasks. And complaints if they did not have the time or if they did not stay a bit longer to get everything done.The extra tasks would become part of their duties.
A given amount of paid time and a specific list of tasks is the only fair way to hire a cleaner. They look at the the tasks and at the time, and if they are happy with the offer they take the job. If on some days it takes them less time, so be it.
I have worked as a cleaner several years and I would say that for 3 to 4 rooms, plus ironing and washing for 3 to 4 people, done twice a week, two hours split are just about right.
Maybe at times there will be 20 min per week to spare, and that's fine too.
Jobs are taken with time to spare, it's normal and fair.
It seems to me that the OP tried with the cleaner first, who understably declined, and then tried to have her husband force the cleaner doing more than agreed.
I think the husband did well refusing. What is he supposed to tell the cleaner?
From now on, in the same time you need to do the same plus "stuff" my wife will decide day by day? If I was the cleaner I would refuse, committing to vague duties is not a wise choice. Way better to get in, do the job agreed, and get out.
To be honest, if this whole set up looks like some contractual situation, it is also because of they way the OP frames it.
She said that the cleaner work is not helping her, or them, but her husband only..
So it sounds like she sees her husband's and children' rooms and clothes as not part of the shared housework. They are her husband stuff to sort.out.
The actual housework to share is whatever she and her own children actually use as well (or perhaps just the common areas and the cooking, but not her children rooms?).
I don't doubt that it must be otherwise a family, which is most important thing, but when it comes to housework this setup reminds me more of a flatshare.