Please don't go in hard, you will ruin her beyond all hope!
If you get to the stage where you feel you have no choice but to let her go, please contact The Border Collie Trust GB, they will evaluate and rehabilitate before rehoming her to a home that suits her personality, be it working or sports home. Do not feel bad if you do have to find her a new home.
Kids often make dogs, especially sensitive ones feel uncomfortable through absolutely no fault of their own, and what you and anyone else deems as untoward, unfortunately can be too much for a nervy BC to tolerate without help. Eye contact is a common one, as is any touch to the neck/chest area. It seems unfair, but it is just how some of them are, and without hands on experienced help, it is very hard to advise how to solve the problem.
If it were me, (and I have had a BC just like this RIP Tikki :love) I would for now, until you have been able to seek help allow no physical contact between dog and children.