First and foremost, ignore her advice to "plea guilty with an explanation" - she had straight out lied to you (not a legal advice, just a warning!). A guilty plea with an explanation is still exactly that - a guilty plea. The best course of action to follow would be to plead "not guilty". This way you can get the notes that the police officer wrote about the incident, and see what she wrote. This may (or may not) shed some light on what exactly the officer "saw" on the scene of the accident. Whether or not what she saw is enough evidence to convict you of "Careless Driving" remains to be seen, it gives you some more time to consider the best course of action for yourself - be it preparing your own defense, getting some legal help from a paralegal or a lawyer (I'd pick a paralegal TBH, lawyers deal with other matters most of the time), no matter - you can always "plead guilty with an explanation" after you see the prosecutor (Crown attorney) in your first attendance meeting.
Your chances to win, as in have the entire ticket dismissed, are not all that great to be honest with you. There are some technicalities that can be used to do exactly that, but the chances are slim, and depend on scheduling, disclosure, etc. Having said that, a "not guilty" checkbox leaves a windows of opportunity for you to talk to the crown attorney and agree to a reduced charge in the worst case scenario, and, in this case, near anything will be better than the "Careless Driving". Quite frankly, the collision is enough to raise your insurance rates as it is, so don't count on no increase there whatsoever, but you can at the very least limit the damage done if you can get your ticket reduced. Once again, ticking off "guilty with an explanation" will not get you anywhere close to reducing your ticket.
In short:
1. Plea "not guilty" on your ticket
1.a - ask here if you get any mail that bothers you from the court, or anything you are not sure about (repeat for any step below)
2. File a "Disclosure request" (this site has many references to it, make good use of the "Search" feature provided)
3. See what the disclosure package has in it
4. Post here again with details of what the disclosure said. The more details the better - that excludes your personal details!!!!!!!!!!!!! *I* *DO* *NOT* *WANT* *TO* *KNOW* *WHO* *YOU* *ARE*, *LET* *ALONE* *KNOW* *WHAT* *YOU* *WERE* *CHARGED* *WITH* - this is standard Canada Privacy Act stuff that forbids us, or anyone else, to ask you for that information. Some people (none that I know on this board) are not as scrupulous as that, but this board is not limited to people who have registered either.
5. Get an answer. Read the answer. Act the answer. Something will be clear after you receive (and post) your disclosure.
6. Good luck with having your charge dropped/dismissed/reduced!