
Firstly the toilet training. It sounds like she has the run of the place while you are out, try restricting her access and putting her into one room. Make sure this is not the room where she favours as her toilet area. As she is capable of going for long periods while you are there without messing, I would take up the paper as this will only encourage her. Make sure where she goes is washed with a biological washing powder solution and even a de-odourising pet spray. If she is just weeing I would take a sample to the vets and check she hasn't got cystitus first. If this doesn't work I would even try a cage or pen her in a very small area (I assume you are not away for long periods). This sounds like a habit that needs breaking rather than anything else.
Secondly the nipping of children.....obviously a more serious problem, but if you do not know her background it is possible she has been provoked by children in the past, they may have even been nasty to her. It sounds more like fear as she is fine with children she knows well. I cannot offer any quick fixes here, but carry on as your are doing watching her very carefully and even muzzle her in childrens company to be on the safe side. Again the dog attacks sound fear related, she will need her confidence built up on this one, walking her with dogs you know that will ignore her or be nice to her.....it could be a slow process, but we all fear our dogs being attacked in the park as it can install this type of behaviour in them.
Hopefully someone else may have further suggestions
Good luck
Sandra