I'm not Canadian but I spent 35 years in the insurance industry in the US and I learned a long time ago how to read statutes and apply them to auto accidents and citations.
The following section of The Highway Traffic Act is quoted in its entirety:
Careless driving - 130. Every person is guilty of the offence of driving carelessly who drives a vehicle or street car on a highway without due care and attention or without reasonable consideration for other persons using the highway and on conviction is liable to a fine of not less than $400 and not more than $2,000 or to imprisonment for a term of not more than six months, or to both, and in addition his or her licence or permit may be suspended for a period of not more than two years.
Here's my opinion for the two cents that it's worth.
The person in front of you stopped suddenly.
You stopped suddenly and hit the person in front of you.
That leads me to conclude that you were either driving too fast for conditions or following too closely, either of which is likely an element of negligence but might not be an element of Careless Driving
I found an article that refers to a 1953 case about Careless Driving. It doesn't give a citation. Maybe your paralegal can look it up.
To qualify as careless, the Ontario Court of Appeal held in a 1953 case, the driving must be considered a breach of duty to the public and deserving of punishment.
"[T]he test, where an accident has occurred, is not whether, if the accused had used greater care or skill, the accident would not have happened. It is whether it is proved beyond reasonable doubt that the accused, in the light of existing circumstances of which he was aware or of which a driver exercising ordinary care should have been aware, failed to use the care and attention or to give to other persons using the highway the consideration that a driver of ordinary care would have used or given in the circumstances."
The article goes on to say:
Several principles have emerged over the years from court rulings on careless driving:
The standard against which the defendant's driving must be measured is not one of perfection. The driving of the defendant must be measured against a reasonable standard or skill, what an ordinary person would do.
A momentary lapse or a simple error in judgment is insufficient to justify a conviction for careless driving.
Where an accident has occurred, the fact that serious injury or death has resulted is not, except in unusual cases, relevant to an assessment of whether there has been a departure from the standard of care which would justify a finding of careless driving.
Mere inadvertent negligence will not necessarily support a conviction for careless driving. More than a bare act of negligence must be proven.
It's interesting to note that the state must prove Careless Driving "beyond reasonable doubt."
It looks like, under Canadian law, you have the possibility of being acquitted based on this little bit of research. I think that the state would have to show ongoing careless behavior for an interval prior to the impact, like if there were witnesses to you driving to fast or riding the bumpers of the cars in front of you. That would be a slam dunk for the state. In the absence of that kind of testimony you might be in good shape.
Of course, there's no way to predict the outcome. It's up to you to make the decision as to whether to fight it or seek a plea bargain.
I do suggest, however, that you have your paralegal find several appellate decisions where Careless Driving convictions were overturned (or not) and see what criteria the court applied to the incident.
That'll give you a better idea of your chances.