Do you really think the children should be removed, Aeroflot? The op has said that they have a good mother. Removing them from a situation that can easily be managed would do more harm than good.
gentlehoney, with specific reference to this bit
"removing them from a situation that can be easily managed"
what gives you the idea that this situation can be easily managed? what are you basing that on apart from wishful thinking? I have quite a bit of experience of animal hoarders and none of them, not one single one of them, was "easily managed".
There is a possibility that SS approach the woman mentioned in the OP, asses the situation, and tell the woman she has a week to rehome the animals and get the house & garden into a fit enough state for the children. And it is possible that the woman says " gee you're right ss, I will get on to the rspca today, make sure the pets are all in a shelter by the weekend, then spend 3 days cleaning house and garden, and rest assured I won't ever do this again. And they all live happily ever after and the problem is well and truly solved.
Then there is the other possibility. The one that is far more likely to happen. That she is forced to rehome the majority of her pets, that she is forced to clean the house and garden up. Then when SS get off her back, she goes back to hoarding animals. She wont go out one day and come home with 7 dogs and 4 cats. No, more likely she will get one kitten, but it will be lonely, so she'll go out to get it a friend. Then when she gets to home with free kittens there are 3 left in the litter and she can't possibly leave them behind, so she takes all 3. Then the week after that she will see a lovely little mild mannered dog being rehomed on facebook, and she will take that too. Then the wee boy down the road who has got fed up of his rabbits, she'll have them too. Then she will realise that her little mild mannered dog needs a friend, that he is lonely, and lo and behold as luck would have it, there is dog being offered for free on gumtree, a cute one it is too. So she'll take that dog too. And so on and so forth.
Nothing about animal hoarding is "easily managed". Nothing. Yes a temporary fix is easy enough to achieve (all it takes is a rspca van to remove the pets, and a few friends and family to help blitz the home), but you must accept that is all it is - a temporary fix.
Until whatever is driving her to hoard animals (and driving her to prioritise her pets above her children) is addressed, I can practically guarantee you this situation won't be fixed.
I think you live in a world where with a bit of sparkly rainbow thinking and few unicorns to help out that everything is nice and easy to fix and the world is a nice easy place if only we all saw it the way you do. In the real world.... try volunteering for a few hours a week in an animal shelter, and I am sure within a year you'll have an opinion that is more in line with the reality of how things really are.