Got rear-ended and was found at fault!

My Wife was driving my son to daycare on her way to work. She was on a freeway with 45mph speed limit. She was in the right most lane, had her turn signal on and slowed down to take the right turn in to the daycare facility. She was rear-ended and her car slid and run up a curb. The other car's front end was destroyed and it caught on fire.

The police arrived to the scene. This is my wife's first car accident and she was in shock. They asked her what happened and she told them the entire thing. There was a witness at the scene who also said that the driver that hit her was at fault. At this point, we were confident that the police would find them at fault. But then the police officer came to us and said that 'we think you had slowed down to take the turn and caused traffic obstruction so we find you at fault her looking at the angle of impact and the damage' (her car was hit right in the middle, the other car had damage on the front passanger side). We were shocked, we have no idea how they came to that conclusion. They further said its usually the insurance companies who further decide amongst themselves who they think is at fault and will be paying. So we left it at that.

Now we just received a traffic ticket citing 'Careless driving: operate M.V causing property damage' and a court appearance is required. We get legal shield services through our employer.

My question is: How likely is it that we might be able to get this ticket dismissed? Is it better to hire a local lawyer to fight the ticket or should we go with the lawyer from legal shield as it might cost us less? Thanks.

Location: New Jersey