I would say she is a slightly nervous dog, Everything is here in this sentence

............ definitely not Cocker rage, nothing like........ but fear, fear, leads to aggression, avoidance, nervousness and submission, she'll will use any and
all of these.
Dogs know that children are children they are not looked upon in the same way as an adult, so will not be deemed with the same respect unless there is a very special bond.
There is no way of knowing 4 years on, whether this is a genetic temperament issue that is just part of the dogs character, (it may well be) or an issue caused in the way she has been raised with your children and socialised. Cockers should be bomb proof, many are not due to their rearing, it is impossible to pinpoint at the age of 4 years now the reasons why? For now......it is her........
What you do know is that you have a dog with a moulded character now, which
can be nervous and snappy, when provoked, (it may not take much to do that) I suggest getting books which will help you pinpoint a dogs body language, it will be of great help to you here.
You can only make life easier for all of you, by accepting she cannot be spooked, cannot have anyone but her adult owner move her, must never be touched when sleeping or have anyone moving too fast or jumping in front or behind her. She needs reassurance from you at all times of what is happening and what is expected of her.
You cannot shout at her or have raised voices, (not saying you do, but just pointing it out.

)
If you keep within these rules and remember she is a dog with 'special needs', due to a nervous disposition, you'll all get along just fine and live happily together.

Personally, I would deflect this nervousness into some fun and games, whistle training, playing with balls and dummies, there are plenty of games for her to play with you all, give her something to think about and enjoy. (I know she is not a Working Cocker, but Show Cockers still enjoy doing these things too)
I hope that things will get better,