I really sympathise with your situation ETavernor. You have been used to a placid, docile cocker who would tolerate anything and used your experience and judgement to get another and you are finding its temperament is, presently at least, very different. There are plently of naturally tolerant dogs out there, that was my former experience too, of dogs (and puppies) that would let children lift them, play around them and with them and fall into them without batting an eyelid. But your dog is not one of those dogs. And then you come to this forum for support and have to read some responses seeming to imply it is a problem with your children for accidentally falling on your dog, or with you, for not having the superhuman powers to control and prevent your children from accidentally falling.
I expect you got your dog expecting her to become a part of your family and you are now seeing that actually, limiting her contact with your children might presently be the safest option. And you might feel torn - because this was not how you were expecting to live and what does that mean for the future? And how will your dog begin to learn more manageable responses if you take her out of these situations altogether? Like I say, I really feel for you, we have had a similarly tough time with our young cocker but we are an adult household. We use a combination of avoiding known big triggers and attempting to desensitize him to situations - this involves gradually exposing him and rewarding good responses (or the absence of negatve responses!) He didn't like being picked up either but we now lift him 3 times a day and he is perfectly happy - this was a long, arduous process of treating him, and we are not being complacent - we do this every day in case he lapses back to his previous response. The same with leading him round with a hand on his collar which he hated and snapped at us over - we repeat this daily as well. But as adults we can make that informed decision ourselves, knowing there was an element of personal risk to us as we began that process - exposing children to a similar process of exposure is quite a different question. If it helps in any way our dog is definitely getting better over time and is more able to inhibit his instinctive responses.
I think you are doing the right thing in getting a behaviourist in, and until you feel you have got some good professional advice it does sound like the wisest thing to do would be to limit contact with the children, especially preventing those situations that you know might trigger a response. Your dog is not a bad dog, your children aren't bad children and you are not a bad mother or dog owner - you're just all in a difficult situation right now and I wish you the best of luck with it.