Keeping track of where your resume has been sent/presented is your responsibility.
When a recruiter asks which companies you have already approached, or how many different recruiters you are working with, you can either be honest or play coy. Just realize that not disclosing the truth could come back to haunt you. Duplicate referrals/representation can cause confusion, and if this is the only way you feel you can get complete market coverage, then you’re not doing enough on your own to maintain traction.
Recruiters aren't naive, and they expect you to have other relationships. But putting them at odds with each other and their clients will not make you the “hot” candidate, it will make you look untrustworthy and unprofessional.
If you do end up declining a hard-fought/hard-won offer; tell your recruiter first! If you go over them to the hiring manager, you risk damaging their relationship, too. The egg on their face will last a very long time, and they won’t easily forget the person who broke that shell.